# Engineering Mechanics MCQ Questions & Answers

Engineering Mechanics MCQs : This section focuses on the "Engineering Mechanics". These Multiple Choice Questions (MCQs) should be practiced to improve the Engineering Mechanics skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

A body of weight W is required to move up on rough inclined plane whose angle of inclination with the horizontal is α. The effort applied parallel to the plane is given by(where μ = tanφ = Coefficient of friction between the plane and the body.)

A. P = W tanα
B. P = W tan(α + φ)
C. P = W (sinα + μcosα)
D. P = W (cosα + μsinα)

Question 2

A body will begin to move down an inclined plane if the angle of inclination of the plane is __________ the angle of friction.

A. equal to
B. less than
C. greater than

Question 3

A redundant frame is also called __________ frame.

A. perfect
B. imperfect
C. deficient

Question 4

A resultant force is a single force which produces the same effect as produced by all the given forces acting on a body.

A. TRUE
B. FALSE

Question 5

A smooth cylinder lying on its convex surface remains in __________ equilibrium.

A. stable
B. unstable
C. neutral

Question 6

According to principle of conservation of energy, the total momentum of a system of masses in any direction remains constant unless acted upon by an external force in that direction.

A. TRUE
B. FALSE

Question 7

Coefficient of friction is the ratio of the limiting friction to the normal reaction between the two bodies.

A. Yes
B. No

Question 8

During elastic impact, the relative velocity of the two bodies after impact is __________ the relative velocity of the two bodies before impact.

A. equal to
B. equal and opposite to
C. less than
D. greater than

Question 9

If a number of forces are acting at a point, theirresultant will be inclined at an angle θ with the horizontal, such that

A. tan θ = ∑H/∑V
B. tan θ = ∑V/∑H
C. tan θ = ∑Vx∑H

Question 10

If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is

A. 30°
B. 60°
C. 90°
D. 120°

Question 11

If two blocks of equal mass are attached to the two ends of a light string and one of the blocks is placed over a smooth horizontal plane while the other is hung freely after passing over a smooth pulley, then the two blocks will have some motion.

A. Agree
B. Disagree

Question 12

If two bodies having masses m1 and m2 (m1>m2) have equal kinetic energies, the momentum of body having mass m1 is __________ the momentum of body having mass m2.

A. equal to
B. less than
C. greater than

Question 13

Moment of inertia of a circular section about an axis perpendicular to the section is

A. πd3/16
B. πd3/32
C. πd4/32
D. πd4/64

Question 14

Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its C.G. and parallel to the base, is

A. bh3/4
B. bh3/8
C. bh3/12
D. bh3/36

Question 15

One watt is equal to

A. 0.1 joule/s
B. 1 joule/s
C. 10 joules/s
D. 100 joules/s

Question 16

Static friction is always __________ dynamic friction.

A. equal to
B. less than
C. greater than

Question 17

The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction. This is known as

A. principle of independence of forces
B. principle of resolution of forces
C. principle of transmissibility of forces
D. none of these

Question 18

The angle between two forces when the resultant is maximum and minimum respectively are

A. 0° and 180°
B. 180° and 0°
C. 90° and 180°
D. 90° and 0°

Question 19

The angle of inclination of a vehicle when moving along a circular path __________ upon its mass.

A. depends
B. does not depend

Question 20

The bodies which rebound after impact are called

A. inelastic bodies
B. elastic bodies
C. neither elastic nor inelastic bodies
D. none of these

Question 21

The centre of gravity of an equilateral triangle with each side a, is __________ from any of the three sides.

A. 3a/2
B. 23a
C. a/23
D. 32a

Question 22

The coefficient of restitution for elastic bodies is one.

A. Correct
B. Incorrect

Question 23

The distance, between the point of projection and the point where the projectile strikes the ground, is known as range.

A. Correct
B. Incorrect

Question 24

The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.

A. equal to
B. less than
C. greater than

Question 25

The force which acts along the radius of a circle and directed away from the centre of the circle is called centrifugal force.

A. Agree
B. Disagree

Question 26

The friction experienced by a body, when in motion, is known as

A. rolling friction
B. dynamic friction
C. limiting friction
D. static friction

Question 27

The maximum frictional force, which comes into play, when a body just begins to slide over the surface of the other body, is known as

A. static friction
B. dynamic friction
C. limiting friction
D. coefficient of friction

Question 28

The mechanical advantage of a lifting machine is the ratio of

A. distance moved by effort to the distance moved by load
B. load lifted to the effort applied
C. output to the input
D. all of the above

Question 29

The path of the projectile is a parabola.

A. TRUE
B. FALSE

Question 30

The range of a projectile is maximum, when the angle of projection is

A. 30°
B. 45°
C. 60°
D. 90°

Question 31

The range of projectile on a downward inclined plane is __________ the range on upward inclined plane for the same velocity of projection and angle of projection.

A. less than
B. more than
C. equal to

Question 32

The term 'force' may be defined as an agent which produces or tends to produce, destroys or tends to destroy motion.

A. Agree
B. Disagree

Question 33

The total time taken by a projectile to reach maximum height and to return back to the ground, is known as time of flight.

A. Yes
B. No

Question 34

The triangle law of forces states that if two forces acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle taken in order, then their resultant may be represented in magnitude and direction by the third side of a triangle, taken in opposite order.

A. TRUE
B. FALSE

Question 35

The unit of angular acceleration is

A. N-m
B. m/s
C. m/s2

Question 36

The velocity ratio in case of an inclined plane inclined at angle θ to the horizontal and weight being pulled up the inclined plane by vertical effort is

A. sin θ
B. cos θ
C. tan θ
D. cosec θ

Question 37

Two balls of equal mass and of perfectly elastic material are lying on the floor. One of the ball with velocity v is made to struck the second ball. Both the balls after impact will move with a velocity

A. v
B. v/2
C. v/4
D. v/8

Question 38

two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20 N. It the line of action of the resultant is 6 mm from any given force, the two forces are

A. 15 N and 5 N
B. 20 N and 5 N
C. 15 N and 15 N
D. none of these

Question 39

When a particle moves along a circular path with uniform velocity, there will be no tangential acceleration.

A. Correct
B. Incorrect

Question 40

When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as

A. simple pendulum
B. compound pendulum
C. torsional pendulum
D. second's pendulum

Question 41

Which of the following is an equation of linear motion?(where, u and v = Initial and final velocity of the body, a = Acceleration of the body, and s = Displacement of the body in time t seconds.)

A. v = u + a.t
B. s = u.t + 1/2 a.t2
C. v2 = u2+2a.s
D. all of these

Question 42

Work done is said to be zero, when

A. some force acts on a body, but displacement is zero
B. no force acts on a body but some displacement takes place
C. either (a) or (b)
D. none of the above

Question 43

The equivalent length of a simple pendulum which gives the same frequency as compound pendulum is

A. h/(kG² + h²)
B. (kG² + h²)/h
C. h²/(kG² + h²)
D. (kG² + h²)/h²

Question 44

When the lift is moving upwards with some acceleration, the pressure exerted by a man is __________ to its acceleration.

A. Directly proportional
B. Inversely proportional
C. Cube root
D. None of these

Question 45

The force required to move the body up the plane will be minimum if it makes an angle with the inclined plane __________ the angle of friction.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 46

Angle of friction is the

A. Angle between normal reaction and the resultant of normal reaction and the limiting friction
B. Ratio of limiting friction and normal reaction
C. The ratio of minimum friction force to the friction force acting when the body is just about to move
D. The ratio of minimum friction force to friction force acting when the body is in motion

Question 47

If tension in the cable supporting a lift moving downwards is half the tension when it is moving upwards, the acceleration of the lift is

A. g/2
B. g/3
C. g/4
D. None of these

Question 48

A particle moves along a straight line such that distance (x) traversed in 't' seconds is given by x = t² (t - 4), the acceleration of the particle will be given by the equation

A. 6t² - 8t
B. 3t² + 2t
C. 6f - 8
D. 6f - 4

Question 49

When two elastic bodies collide with each other,

A. The two bodies will momentarily come to rest after collision
B. The two bodies tend to compress and deform at the surface of contact
C. The two bodies begin to regain their original shape
D. All of the above

Question 50

A number of forces acting at a point will be in equilibrium, if

A. All the forces are equally inclined
B. Sum of all the forces is zero
C. Sum of resolved parts in the vertical direction is zero (i.e. ∑V = 0)
D. None of these

Question 51

The moment of inertia of a square of side (a) about an axis through its center of gravity is

A. a4/4
B. a4/8
C. a4/12
D. a4/36

Question 52

The maximum mechanical advantage of a lifting machine is

A. 1 + m
B. 1 - m
C. 1 / m
D. m

Question 53

According to law of triangle of forces

A. Three forces acting at a point will be in equilibrium
B. Three forces acting at a point can be represented by a triangle, each side being proportional to force
C. If three forces acting upon a particle are represented in magnitude and direction by the sides of a triangle, taken in order, they will be in equilibrium
D. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two

Question 54

A smooth cylinder lying on its convex surface remains in __________ equilibrium.

A. Stable
B. Unstable
C. Neutral
D. None of these

Question 55

Center of percussion is

A. The point of C.G.
B. The point of metacenter
C. The point of application of the resultant of all the forces tending to cause a body to rotate about a certain axis
D. Point of suspension

Question 56

The linear velocity of a body rotating at ω rad/s along a circular path of radius r is given by

A. ω/r
B. ω.r
C. ω²/r
D. ω².r

Question 57

For a self locking machine, the efficiency must be

A. Equal to 50%
B. Less than 50%
C. Greater than 50%
D. 100%

Question 58

Coefficient of friction depends upon

A. Area of contact only
B. Nature of surface only
C. Both (A) and (B)
D. None of these

Question 59

Coefficient of friction is the

A. Angle between normal reaction and the resultant of normal reaction and the limiting friction
B. Ratio of limiting friction and normal reaction
C. The friction force acting when the body is just about to move
D. The friction force acting when the body is in motion

Question 60

Pick up the incorrect statement from the following:

A. The C.G. of a circle is at its centre
B. The C.G. of a triangle is at the intersection of its medians
C. The C.G. of a rectangle is at the intersection of its diagonals
D. The C.G. of a semicircle is at a distance of r/2 from the centre

Question 61

The ratio of limiting friction and normal reaction is known as

A. Coefficient of friction
B. Angle of friction
C. Angle of repose
D. Sliding friction

Question 62

Least force required to draw a body up the inclined plane is W sin (plane inclination + friction angle) applied in the direction

A. Along the plane
B. Horizontally
C. Vertically
D. At an angle equal to the angle of friction to the inclined plane

Question 63

Non-coplanar concurrent forces are those forces which

A. Meet at one point, but their lines of action do not lie on the same plane
B. Do not meet at one point and their lines of action do not lie on the same plane
C. Meet at one point and their lines of action also lie on the same plane
D. Do not meet at one point, but their lines of action lie on the same plane

Question 64

Coplanar concurrent forces are those forces which

A. Meet at one point, but their lines of action do not lie on the same plane
B. Do not meet at one point and their lines of action do not lie on the same plane
C. Meet at one point and their lines of action also lie on the same plane
D. Do not meet at one point, but their lines of action lie on the same plane

Question 65

Non-coplanar non-concurrent forces are those forces which

A. Meet at one point, but their lines of action do not lie on the same plane
B. Do not meet at one point and their lines of action do not lie on the same plane
C. Do not meet at one point but their lines of action lie on the same plane
D. None of the above

Question 66

A pendulum which executes one beat per second is known as

A. Simple pendulum
B. Compound pendulum
C. Torsional pendulum
D. Second's pendulum

Question 67

D' Alembert's principle is used for

A. Reducing the problem of kinetics to equivalent statics problem
B. Determining stresses in the truss
C. Stability of floating bodies
D. Designing safe structures

Question 68

Centre of gravity of a solid cone lies on the axis at the height

A. One fourth of the total height above base
B. One third of the total height above base
C. One-half of the total height above base
D. Three eighth of the total height above the base

Question 69

In the lever of third order, load ‘W’, effort ‘P’ and fulcrum ‘F’ are oriented as follows

A. W between P and F
B. F between W and P
C. P between W and F
D. W, P and F all on one side

Question 70

The ideal angle of banking provided on the curves on roads depends upon

A. Weight of the vehicle
B. (Velocity)2 of the vehicle
C. Nature of the road surface
D. Coefficient of friction between the road and vehicle contact point

Question 71

The power developed by a body acted upon by a torque 'T' Newton meter (N - m) and revolving at ω radian/s is given by

A. T.ω (in watts)
B. T.ω/60 (in watts)
C. T.ω/75 (in kilowatts)
D. T.ω/4500 (in kilowatts)

Question 72

From a circular plate of diameter 6 cm is cut out a circle whose diameter is a radius of the plate. Find the e.g. of the remainder from the centre of circular plate

A. 0.5 cm
B. 1.0 cm
C. 1.5 cm
D. 2.5 cm

Question 73

If rain is falling in the opposite direction of the movement of a pedestrian, he has to hold his umbrella

A. More inclined when moving
B. Less inclined when moving
C. More inclined when standing
D. Less inclined when standing

Question 74

According to Newton's first law of motion,

A. Everybody continues in its state of rest or of uniform motion, in a straight line, unless it is acted upon by some external force
B. The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction, in which the force acts
C. To every action, there is always an equal and opposite reaction
D. None of the above

Question 75

The three forces of 100 N, 200 N and 300 N have their lines of action parallel to each other but act in the opposite directions. These forces are known as

A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Like parallel forces
D. Unlike parallel forces

Question 76

In order to completely specify angular displacement by a vector, it must fix

A. Direction of the axis of rotation
B. Magnitude of angular displacement
C. Sense of angular displacement
D. All of these

Question 77

The force, by which the body is attracted, towards the center of the earth, is called

A. Impulsive force
B. Mass
C. Weight
D. Momentum

Question 78

In actual machines, mechanical advantage is _________ velocity ratio.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 79

Whenever a force acts on a body and the body undergoes a displacement, then

A. Work is said to be done
B. Power is being transmitted
C. Body has kinetic energy of translation
D. None of these

Question 80

Which of the following is not a scalar quantity?

A. Mass
B. Volume
C. Density
D. Acceleration

Question 81

Which of the following is not a vector quantity?

A. Weight
B. Velocity
C. Acceleration
D. Force

Question 82

Which of the following is not the unit of power?

A. kW (kilowatt)
B. hp (horse power)
C. kcal/sec
D. kcal/kg sec

Question 83

Pick up wrong statement about friction force for dry surfaces. Friction force is

A. Proportional to normal load between the surfaces
B. Dependent on the materials of contact surface
C. Proportional to velocity of sliding
D. Independent of the area of contact surfaces

Question 84

A body will begin to move down an inclined plane if the angle of inclination of the plane is _________ the angle of friction.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 85

The center of gravity of a semi-circle lies at a distance of __________ from its base measured along the vertical radius.

A. 3r/ 8
B. 4r/ 3π
C. 8r/3
D. 3r/4π

Question 86

The rate of change of displacement of a body is called

A. Velocity
B. Acceleration
C. Momentum
D. None of these

Question 87

Effect of a force on a body depends upon

A. Magnitude
B. Direction
C. Position or line of action
D. All of the above

Question 88

If the gravitational acceleration at any place is doubled, then the weight of a body will be

A. g/2
B. g
C. √2.g
D. 2g

Question 89

A machine having an efficiency less than 50%, is known as

A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine

Question 90

Which is the correct statement about law of polygon of forces?

A. If any number of forces acting at a point can be represented by the sides of a polygon taken in order, then the forces are in equilibrium
B. If any number of forces acting at a point can be represented in direction and magnitude by the sides of a polygon, then the forces are in equilibrium
C. If a polygon representing forces acting at a point is closed then forces are in equilibrium
D. If any number of forces acting at a point can be represented in direction and magnitude by the sides of a polygon taken in order, then the forces are in equilibrium

Question 91

Which of the following is an equation of linear motion?(where, u and v = Initial and final velocity of the body, a = Acceleration of the body, and s = Displacement of the body in time t seconds.)

A. v = u + a.t
B. s = u.t + ½ a.t2
C. v2 = u2 + 2a.s
D. All of these

Question 92

The moment of inertia of a thin disc of mass ‘m’ and radius ‘r’, about an axis through its center of gravity and perpendicular to the plane of the disc is

A. mr²/2
B. mr²/4
C. mr²/6
D. mr²/8

Question 93

If three forces acting in different planes can be represented by a triangle, these will be in

A. Non-equilibrium
B. Partial equilibrium
C. Full equilibrium
D. Unpredictable

Question 94

The velocity ratio of a differential wheel and axle with 'D' as the diameter of effort wheel and d1 and d2 as the diameters of larger and smaller axles respectively, is

A. D/(d₁ + d₂)
B. D/(d₁ - d₂)
C. 2D/(d₁ + d₂)
D. 2D/(d₁ - d₂)

Question 95

A framed structure is perfect if it contains members equal to (Where, n = number of joints in a frame)

A. 2n³
B. 2n
C. n²
D. 3n²

Question 96

The velocity ratio of a simple wheel and axle with D and d as the diameters of effort wheel and load axle, is

A. D + d
B. D - d
C. D × d
D. D / d

Question 97

A screw jack used for lifting the loads is

A. A reversible machine
B. A non-reversible machine
C. An ideal machine
D. None of these

Question 98

A particle inside a hollow sphere of radius r, having coefficient of friction µ can rest up to height of

A. r/2
B. r/A
C. r/3
D. 0.134 r

Question 99

The centre of gravity of a uniform lamina lies at

A. The centre of heavy portion
B. The bottom surface
C. The midpoint of its axis
D. All of the above

Question 100

The range of projectile on a downward inclined plane is ________ the range on upward inclined plane for the same velocity of projection and angle of projection.

A. Less than
B. More than
C. Equal to
D. None of These

Question 101

The coefficient of restitution for inelastic bodies is

A. Zero
B. One
C. Between zero and one
D. More than one

Question 102

A flywheel on a motor goes from rest to 1000 rpm in 6 sec. The number of revolutions made is nearly equal to

A. 25
B. 50
C. 100
D. 250

Question 103

Which of the following is a scalar quantity?

A. Force
B. Speed
C. Velocity
D. Acceleration

Question 104

Which of the following is a vector quantity?

A. Energy
B. Mass
C. Momentum
D. Angle

Question 105

Which of the following statement is correct?

A. The periodic time of a particle moving with simple harmonic motion is the time taken by a particle for one complete oscillation
B. The periodic time of a particle moving with simple harmonic motion is directly proportional to its angular velocity
C. The velocity of the particle moving with simple harmonic motion is zero at the mean position
D. The acceleration of the particle moving with simple harmonic motion is maximum at the mean position

Question 106

Which of the following statement is correct?

A. The kinetic energy of a body during impact remains constant
B. The kinetic energy of a body before impact is equal to the kinetic energy of a body after impact
C. The kinetic energy of a body before impact is less than the kinetic energy of a body after impact
D. The kinetic energy of a body before impact is more than the kinetic energy of a body after impact

Question 107

The resultant of two equal forces ‘P’ making an angle ‘θ’, is given by

A. 2P sinθ/2
B. 2P cosθ/2
C. 2P tanθ/2
D. 2P cotθ/2

Question 108

A framed structure is perfect, if the number of members are __________ (2j - 3), where j is the number of joints.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 109

If a number of forces are acting at a point, their resultant is given by

A. (∑V)2 + (∑H)2
B. √[(∑V)2 + (∑H)2]
C. (∑V)2 +(∑H)2 +2(∑V)(∑H)
D. √[(∑V)2 +(∑H)2 +2(∑V)(∑H)]

Question 110

The linear acceleration (a) of a body rotating along a circular path of radius (r) with an angular acceleration of α rad/s2, is

A. a = α/ r
B. a = α.r
C. a = r / α
D. None of these

Question 111

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. IP) is given by(where, A = Area of the section, IG = Moment of inertia of the section about an axis passing through its C.G., and h = Distance between C.G. and the parallel axis.)

A. IP = IG + Ah2
B. IP = IG - Ah2
C. IP = IG / Ah2
D. IP = Ah2 / IG

Question 112

The friction experienced by a body, when at rest, is known as

A. Static friction
B. Dynamic friction
C. Limiting friction
D. Coefficient of friction

Question 113

The coefficient of friction depends upon

A. Nature of surfaces
B. Area of contact
C. Shape of the surfaces
D. All of the above

Question 114

For any system of coplanar forces, the condition of equilibrium is that the

A. Algebraic sum of the horizontal components of all the forces should be zero
B. Algebraic sum of the vertical components of all the forces should be zero
C. Algebraic sum of moments of all the forces about any point should be zero
D. All of the above

Question 115

Center of gravity of a thin hollow cone lies on the axis at a height of

A. One-fourth of the total height above base
B. One-third of the total height above base
C. One-half of the total height above base
D. Three-eighth of the total height above the base

Question 116

The time of flight of a projectile on downward inclined plane depends upon

A. Angle of projection
B. Angle of inclination of the plane
C. Both (A) and (B)
D. None of these

Question 117

In a single threaded worm and worm wheel, the number of teeth on the worm is 50. The diameter of the effort wheel is 100 mm and that of load drum is 50 mm. The velocity ratio is

A. 50
B. 100
C. 200
D. 400

Question 118

The potential energy of a vertically raised body is __________ the kinetic energy of a vertically falling body.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 119

Which of the following is not the unit of energy?

A. kg m
B. kcal
C. Watt
D. Watt hours

Question 120

Which one of the following statements is not correct?

A. The tangent of the angle of friction is equal to coefficient of friction
B. The angle of repose is equal to angle of friction
C. The tangent of the angle of repose is equal to coefficient of friction
D. The sine of the angle of repose is equal to coefficient to friction

Question 121

The forces, whose lines of action are parallel to each other and act in the same directions, are known as

A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Like parallel forces
D. Unlike parallel forces

Question 122

The velocity ratio in case of an inclined plane inclined at angle 'θ' to the horizontal and weight being pulled up the inclined plane by vertical effort is

A. sinθ
B. cosθ
C. tanθ
D. cosecθ

Question 123

The skidding away of the vehicle on a level circular path can be avoided if the force of friction between the wheels and the ground is __________ the centrifugal force.

A. Less than
B. Greater than
C. Equal to
D. None of these

Question 124

The efficiency of a lifting machine is the ratio of

A. Output to the input
B. Work done by the machine to the work done on the machine
C. Mechanical advantage to the velocity ratio
D. All of the above

Question 125

When the spring of a watch is wound, it will possess

A. Strain energy
B. Kinetic energy
C. Heat energy
D. Electrical energy

Question 126

The frequency of oscillation of a compound pendulum is (where kG = Radius of gyration about the centroidal axis, and h = Distance between the point of suspension and C.G. of the body.)

A. 2π. √(gh/kG² + h²)
B. 2π. √(kG² + h²/gh)
C. 1/2π. √(gh/kG² + h²)
D. 1/2π. √(kG² + h²/gh)

Question 127

The velocity of a particle (v) moving with simple harmonic motion, at any instant is given by (where, r = Amplitude of motion, and y = Displacement of the particle from mean position.)

A. ω.√(y² - r²)
B. ω.√(r² - y²)
C. ω².√(y² - r²)
D. ω².√(r² - y²)

Question 128

If a given force (or a given system of forces) acting on a body __________ the position of the body, but keeps it in equilibrium, then its effect is to produce internal stress in the body.

A. Change
B. Does not change
C. Changes periodically
D. None of these

Question 129

The maximum height of a projectile on a horizontal plane, is

A. u² sin²α/2g
B. u² cos²α/2g
C. u² sin²α/g
D. u² cos²α/g

Question 130

The maximum frictional force which comes into play when a body just begins to slide over another surface is called

A. Limiting friction
B. Sliding friction
C. Rolling friction
D. Kinematic friction

Question 131

A heavy string attached at two ends at same horizontal level and when central dip is very small approaches the following curve

A. Circular arc
B. Parabola
C. Hyperbola
D. Elliptical

Question 132

The moment of inertia of a solid sphere of mass ‘m’ and radius ‘r’ is

A. 2mr²/3
B. 2mr²/5
C. mr²
D. mr²/2

Question 133

According to principle of transmissibility of forces, the effect of a force upon a body is

A. maximum when it acts at the center of gravity of a body
B. different at different points in its line of action
C. the same at every point in its line of action
D. minimum when it acts at the C.G. of the body

Question 134

Which of the following is the example of lever of first order?

A. Arm of man
B. Pair of scissors
C. Pair of clinical tongs
D. All of the above

Question 135

The resultant of the following three couples 20 kg force, 0.5 m arm, +ve sense 30 kg force, 1 m arm, -ve sense 40 kg force, 0.25 m arm, +ve sense having arm of 0.5 m will be

A. 20 kg, -ve sense
B. 20 kg, + ve sense
C. 10 kg, + ve sense
D. 10 kg, -ve sense

Question 136

A couple produces

A. Translatory motion
B. Rotational motion
C. Combined translatory and rotational motion
D. None of the above

Question 137

A force acting on a body may

A. Change its motion
B. Balance the other forces acting on it
C. Retard its motion
D. All of the above

Question 138

A force while acting on a body may

A. Change its motion
B. Balance the forces, already acting on it
C. Give rise to the internal stresses in it
D. All of these

Question 139

Mass moment of inertia of a thin rod about its one end is ___________ the mass moment of inertia of the same rod about its mid-point

A. Same as
B. Twice
C. Thrice
D. Four times

Question 140

On a ladder resting on smooth ground and leaning against vertical wall, the force of friction will be

A. Towards the wall at its upper end
B. Away from the wall at its upper end
C. Upwards at its upper end
D. Downwards at its upper end

Question 141

According to Lami’s theorem

A. The three forces must be equal
B. The three forces must be at 120° to each other
C. The three forces must be in equilibrium
D. If the three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two

Question 142

On the ladder resting on the ground and leaning against a smooth vertical wall, the force of friction will be

A. Downwards at its upper end
B. Upwards at its upper end
C. Perpendicular to the wall at its upper end
D. Zero at its upper end

Question 143

According to principle of moments

A. If a system of coplanar forces is in equilibrium, then their algebraic sum is zero
B. If a system of coplanar forces is in equilibrium, then the algebraic sum of their moments about any point in their plane is zero
C. The algebraic sum of the moments of any two forces about any point is equal to moment of the resultant about the same point
D. Positive and negative couples can be balanced

Question 144

The velocity of a body on reaching the ground from a height h, is

A. 2.√(gh)
B. √(gh)
C. √(2gh)
D. 2g.√h

Question 145

Lami's theorem states that

A. Three forces acting at a point will be in equilibrium
B. Three forces acting at a point can be represented by a triangle, each side being proportional to force
C. If three forces acting upon a particle are represented in magnitude and direction by the sides of a triangle, taken in order, they will be in equilibrium
D. If three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two

Question 146

An ideal machine is one whose efficiency is

A. Between 60 and 70 %
B. Between 70 and 80%
C. Between 80 and 90%
D. 100%

Question 147

Moment of inertia of a circular section about its diameter (d) is

A. πd3/16
B. πd3/32
C. πd4/32
D. πd4/64

Question 148

A heavy ladder resting on floor and against a vertical wall may not be in equilibrium, if

A. The floor is smooth, the wall is rough
B. The floor is rough, the wall is smooth
C. The floor and wall both are smooth surfaces
D. The floor and wall both are rough surfaces

Question 149

The range of projectile (R) on an upward inclined plane is

A. g. cos² β/2u². sin (α + β). cos α
B. 2u². sin (α + β). cos α/g. cos² β
C. g. cos² β/2u². sin (α - β). cos α
D. 2u². sin (α - β). cos α/g. cos² β

Question 150

In the equation of virtual work, following force is neglected

A. Reaction of any smooth surface with which the body is in contact
B. Reaction of a rough surface of a body which rolls on it without slipping
C. Reaction at a point or an axis, fixed in space, around which a body is constrained to turn
D. All of the above

Question 151

If a number of forces are acting at a point, their resultant will be inclined at an angle 'θ' with the horizontal, such that

A. tanθ = ΣH/ΣV
B. tanθ = ΣV/ΣH
C. tanθ = ΣV × ΣH
D. tanθ = √(ΣV + ΣH)

Question 152

Which of the following statement is correct?

A. The algebraic sum of the forces, constituting the couple is zero
B. The algebraic sum of the forces, constituting the couple, about any point is the same
C. A couple cannot be balanced by a single force but can be balanced only by a couple of opposite sense
D. All of the above

Question 153

The principle of transmissibility of forces states that, when a force acts upon a body, its effect is

A. Same at every point on its line of action
B. Different at different points on its line of action
C. Minimum, if it acts at the center of gravity of the body
D. Maximum, if it acts at the center of gravity of the body

Question 154

Two coplanar couples having equal and opposite moments

A. Balance each other
B. Produce a couple and an unbalanced force
C. Are equivalent
D. Cannot balance each other

Question 155

The process of finding out the resultant force is called __________ of forces.

A. Composition
B. Resolution
C. Decomposition
D. None of these

Question 156

Limiting force of friction is the

A. Tangent of angle between normal reaction and the resultant of normal reaction and limiting friction
B. Ratio of limiting friction and normal reaction
C. The friction force acting when the body is just about to move
D. The friction force acting when the body is in motion

Question 157

In order to determine the effects of a force, acting on a body, we must know

A. Magnitude of the force
B. Line of action of the force
C. Nature of the force i.e. whether the force is push or pull
D. All of the above

Question 158

Coulomb friction is the friction between

A. Bodies having relative motion
B. Two dry surfaces
C. Two lubricated surfaces
D. Solids and liquids

Question 159

In a screw jack, the effort required to lower the load is __________ the effort required to raise the same load.

A. Less than
B. Equal to
C. More than
D. None of these

Question 160

The slope on the road surface generally provided on the curves is known as

A. Angle of friction
B. Angle of repose
C. Angle of banking
D. None of these

Question 161

Frictional force encountered after commencement of motion is called

A. Limiting friction
B. Kinematic friction
C. Frictional resistance
D. Dynamic friction

Question 162

A pair of smith's tongs is an example of the lever of

A. Zeroth order
B. First order
C. Second order
D. Third order

Question 163

Two balls of equal mass and of perfectly elastic material are lying on the floor. One of the balls with velocity ‘v’ is made to strike the second ball. Both the balls after impact will move with a velocity

A. v
B. v/2
C. v/4
D. v/8

Question 164

A single force and a couple acting in the same plane upon a rigid body

A. Balance each other
B. Cannot balance each other
C. Produce moment of a couple
D. Are equivalent

Question 165

The centre of gravity of an isosceles triangle with base (p) and sides (q) from its base is

A. [√(4p² - q²)]/6
B. (4p² - q²)/6
C. (p² - q²)/4
D. (p² + q²)/4

Question 166

Tangent of angle of friction is equal to

A. Kinetic friction
B. Limiting friction
C. Angle of repose
D. Coefficient of friction

Question 167

The point, through which the whole weight of the body acts, irrespective of its position, is known as

A. Moment of inertia
B. Center of gravity
C. Center of percussion
D. Center of mass

Question 168

Moment of inertia of a triangular section of base (b) and height (h) about an axis passing through its vertex and parallel to the base, is __________ than that passing through its C.G. and parallel to the base.

A. Nine times
B. Six times
C. Four times
D. Two times

Question 169

The resultant of the two forces ‘P’ and ‘Q’ is ‘R’. If ‘Q’ is doubled, the new resultant is perpendicular to ‘P’. Then

A. P = Q
B. Q = R
C. Q = 2R
D. None of these

Question 170

The periodic time (T) is given by (where, ω = Angular velocity of particle in rad/s.)

A. ω/2π
B. 2π/ω
C. 2π × ω
D. π/ω

Question 171

The total momentum of a system of masses (i. e. moving bodies) in any one direction remains constant, unless acted upon by an external force in that direction. This statement is called

A. Newton's first law of motion
B. Newton's second law of motion
C. Principle of conservation of energy
D. Principle of conservation of momentum

Question 172

Moment of inertia of a triangular section of base (b) and height (h) about an axis through its base, is

A. bh3/4
B. bh3/8
C. bh3/12
D. bh3/36

Question 173

The unit of force in S.I. system of units is

A. Dyne
B. Kilogram
C. Newton
D. Watt

Question 174

The centre of percussion is below the centre of gravity of the body and is at a distance equal to

A. h/kG
B. h2/kG
C. kG2/h
D. h × kG

Question 175

The Cartesian equation of trajectory is (where u = Velocity of projection, α = Angle of projection, and x, y = Co-ordinates of any point on the trajectory after t seconds.)

A. y = (gx²/2u² cos²α) + x. tanα
B. y = (gx²/2u² cos²α) - x. tanα
C. y = x. tanα - (gx²/2u² cos²α)
D. y = x. tanα + (gx²/2u² cos²α)

Question 176

The coefficient of friction depends on

A. Area of contact
B. Shape of surfaces
C. Strength of surfaces
D. Nature of surface

Question 177

The velocity ratio of a first system of pulleys with 4 pulleys is

A. 4
B. 8
C. 16
D. 20

Question 178

A lead ball with a certain velocity is made to strike a wall, it falls down, but rubber ball of same mass and with same velocity strikes the same wall, it rebounds. Select the correct reason from the following:

A. Both the balls undergo an equal change in momentum
B. The change in momentum suffered by rubber ball is more than the lead ball
C. The change in momentum suffered by rubber ball is less than the lead ball
D. None of the above

Question 179

A body moves, from rest with a constant acceleration of 5 m per sec. The distance covered in 5 sec is most nearly

A. 38 m
B. 62.5 m
C. 96 m
D. 124 m

Question 180

The moment of inertia of a solid cylinder of mass 'm', radius 'r' and length 'l' about the longitudinal axis or polar axis is

A. mr²/2
B. mr²/4
C. mr²/6
D. mr²/8

Question 181

Forces are called coplanar when all of them acting on body lie in

A. One point
B. One plane
C. Different planes
D. Perpendicular planes

Question 182

The angular velocity (in rad/s) of a body rotating at N revolutions per minute is

A. πN/60
B. πN/180
C. 2πN/60
D. 2πN/180

Question 183

When a body of mass moment of inertia 'I' (about a given axis) is rotated about that axis with an angular velocity to, then the kinetic energy of rotation is

A. Iω
B. Iω2
C. 0.5 Iω
D. 0.5 Iω2

Question 184

A cable with a uniformly distributed load per horizontal meter run will take the following shape

A. Straight line
B. Parabola
C. Hyperbola
D. Elliptical

Question 185

The minimum force required to slide a body of weight 'W' on a rough horizontal plane is

A. W sinθ
B. W cosθ
C. W tanθ
D. None of these

Question 186

The velocity ratio of a differential pulley block with D and d as the diameters of larger and smaller pulley, is

A. D/(D - d)
B. D/(D + d)
C. 2D/(D - d)
D. 2D/(D + d)

Question 187

Which of the following statement is incorrect?

A. A force acting in the opposite direction to the motion of the body is called force of friction
B. The ratio of the limiting friction to the normal reaction is called coefficient of friction
C. A machine whose efficiency is 100% is known as an ideal machine
D. The velocity ratio of a machine is the ratio of load lifted to the effort applied

Question 188

The acceleration of a particle moving with simple harmonic motion, at any instant is given by

A. ω.y
B. ω2.y
C. ω2/y
D. ω3.y

Question 189

The length of a second's pendulum is

A. 94.9 cm
B. 99.4 cm
C. 100 cm
D. 101 cm

Question 190

The law of the machine is (where P = Effort applied to lift the load, m = A constant which is equal to the slope of the line, W = Load lifted, and C = Another constant which represents the machine friction.)

A. P = mW - C
B. P = m/W + C
C. P = mW + C
D. P = C - mW

Question 191

The moment of a force

A. Is the turning effect produced by a force, on the body, on which it acts
B. Is equal to the product of force acting on the body and the perpendicular distance of a point and the line of action of the force
C. Is equal to twice the area of the triangle, whose base is the line representing the force and whose vertex is the point, about which the moment is taken
D. All of the above

Question 192

A machine having an efficiency greater than 50%, is known as

A. Reversible machine
B. Non-reversible machine
C. Neither reversible nor non-reversible machine
D. Ideal machine

Question 193

The motion of a wheel of a car is

A. Purely translation
B. Purely rotational
C. Combined translation and rotational
D. None of these

Question 194

The centre of gravity of a right circular solid cone is at a distance of _________ from its base, measured along the vertical axis.(where h = Height of a right circular solid cone.)

A. h/2
B. h/3
C. h/4
D. h/6

Question 195

The rate of doing work is known as

A. Potential energy
B. Kinetic energy
C. Power
D. None of these

Question 196

Two forces are acting at an angle of 120°. The bigger force is 40 N and the resultant is perpendicular to the smaller one. The smaller force is

A. 20 N
B. 40 N
C. 120 N
D. None of these

Question 197

The time of flight (t) of a projectile on a horizontal plane is given by

A. t = 2u. sinα/g
B. t = 2u. cosα/g
C. t = 2u. tanα/g
D. t = 2u/g.sinα

Question 198

In actual machines

A. Mechanical advantage is greater than velocity ratio
B. Mechanical advantage is equal to velocity ratio
C. Mechanical advantage is less than velocity ratio

Question 199

The term 'Centroid' is

A. The same as centre of gravity
B. The point of suspension
C. The point of application of the resultant of all the forces tending to cause a body to rotate about a certain axis
D. None of the above

Question 200

If three forces acting in one plane upon a rigid body, keep it in equilibrium, then they must either

A. Meet in a point
B. Be all parallel
C. At least two of them must meet
D. All the above are correct

Question 201

In ideal machines

A. Mechanical advantage is greater than velocity ratio
B. Mechanical advantage is equal to velocity ratio
C. Mechanical advantage is less than velocity ratio

Question 202

The unit of angular velocity is

A. m/min
C. Revolutions/min
D. Both (B) and (C)

Question 203

In determining stresses in frames by methods of sections, the frame is divided into two parts by an imaginary section drawn in such a way as not to cut more than

A. Two members with unknown forces of the frame
B. Three members with unknown forces of the frame
C. Four members with unknown forces of the frame
D. Three members with known forces of the frame

Question 204

The unit of force in S.I. units is

A. kilogram
B. Newton
C. Watt
D. Dyne

Question 205

A trolley wire weighs 1.2 kg per meter length. The ends of the wire are attached to two poles 20 meters apart. If the horizontal tension is 1500 kg find the dip in the middle of the span

A. 2.5 cm
B. 3.0 cm
C. 4.0 cm
D. 5.0 cm

Question 206

The unit of work in S.I. units is

A. Newton
B. erg
C. kg-m
D. joule

Question 207

Coplanar non-concurrent forces are those forces which __________ at one point, but their lines of action lie on the same plane.

A. Meet
B. Do not meet
C. Either ‘A’ or ‘B’
D. None of these

Question 208

The weight of a body is due to

A. Gravitational pull exerted by the earth
B. Forces experienced by body in atmosphere
C. Force of attraction experienced by particles
D. Gravitational force of attraction towards the centre of the earth

Question 209

Which of the following do not have identical dimensions?

A. Momentum and impulse
B. Torque and energy
C. Torque and work
D. Moment of a force and angular momentum

Question 210

The wheels of a moving car possess

A. Potential energy only
B. Kinetic energy of translation only
C. Kinetic energy of rotation only
D. Kinetic energy of translation and rotation both

Question 211

If ‘P’ is the force acting on the body, ‘m’ is the mass of the body and ‘a’ is the acceleration of the body, then according to Newton's second law of motion,

A. P + m.a = 0
B. P - m.a = 0
C. P × m.a = 0
D. P/m.a = 0

Question 212

If a number of coplanar forces acting at a point be in equilibrium, the sum of clockwise moments must be __________ the sum of anticlockwise moments, about any point.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 213

The angle of inclination of the plane at which the body begins to move down the plane, is called

A. Angle of friction
B. Angle of repose
C. Angle of projection
D. None of these

Question 214

A body of weight 'W' is required to move up on rough inclined plane whose angle of inclination with the horizontal is 'α'. The effort applied parallel to the plane is given by (where μ = tanφ = Coefficient of friction between the plane and the body.)

A. P = W tanα
B. P = W tan (α + φ)
C. P = W (sinα + μcosα)
D. P = W (cosα + μsinα)

Question 215

If n = number of members and y = number of joints, then for a perfect frame, n = ?

A. 1-2
B. 2-3
C. 3-2
D. 2-4

Question 216

The law of motion involved in the recoil of gun is

A. Newton's first law of motion
B. Newton's second law of motion
C. Newton's third law of motion
D. None of these

Question 217

The velocity ratio for the third system of pulleys is

A. n
B. n²
C. 2n
D. 2n - 1

Question 218

The moment of inertia of a thin rod of mass 'm' and length 'l', about an axis through its centre of gravity and perpendicular to its length is

A. ml2/4
B. ml2/ 6
C. ml2/8
D. ml2/12

Question 219

Dynamic friction as compared to static friction is

A. Same
B. More
C. Less
D. May be less of more depending on nature of surfaces and velocity

Question 220

The center of gravity of a triangle lies at the point of

A. Concurrence of the medians
B. Intersection of its altitudes
C. Intersection of bisector of angles
D. Intersection of diagonals

Question 221

The forces, which meet at one point, but their lines of action do not lie in a plane, are called

A. Coplanar non-concurrent forces
B. Non-coplanar concurrent forces
C. Non-coplanar non-concurrent forces
D. Intersecting forces

Question 222

The maximum efficiency of a lifting machine is

A. 1/m
B. V.R./m
C. m/V.R.
D. 1/(m × V.R.)

Question 223

A. Compression or tension
B. Buckling or shear
C. Shear or tension
D. All of the above

Question 224

Which of the following is the locus of a point that moves in such a manner that its distance from a fixed point is equal to its distance from a fixed line multiplied by a constant greater than one

A. Ellipse
B. Hyperbola
C. Parabola
D. Circle

Question 225

The resultant of two forces P and Q (such that P > Q) acting along the same straight line, but in opposite direction, is given by

A. P + Q
B. P - Q
C. P / Q
D. Q / P

Question 226

The loss of kinetic energy during inelastic impact, is given by (where m1 = Mass of the first body,m2 = Mass of the second body, and u1 and u2 = Velocities of the first and second bodies respectively.)

A. [m₁ m₂/2(m₁ + m₂)] (u₁ - u₂)²
B. [2(m₁ + m₂)/m₁ m₂] (u₁ - u₂)²
C. [m₁ m₂/2(m₁ + m₂)] (u₁² - u₂²)
D. [2(m₁ + m₂)/m₁ m₂] (u₁² - u₂²)

Question 227

In ideal machines, mechanical advantage is __________ velocity ratio.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 228

Tension in the cable supporting a lift is more when the lift is moving __________ with an acceleration.

A. Upwards
B. Downwards
C. Horizontal
D. None of these

Question 229

A force is completely defined when we specify

A. Magnitude
B. Direction
C. Point of application
D. All of the above

Question 230

The amplitude is always __________ radius of the circle.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 231

The C.G. of a solid hemisphere lies on the central radius 3r

A. At distance — from the plane base 3r
B. At distance — from the plane base 3r
C. At distance — from the plane base 3r
D. At distance — from the plane base

Question 232

If the number of pulleys in a system is equal to its velocity ratio, then it is a __________ system of pulleys.

A. First
B. Second
C. Third
D. None of these

Question 233

The forces which meet at one point, but their lines of action __________ on the same plane, are Known as non-coplanar concurrent forces.

A. Lie
B. Do not lie
C. Either A or B
D. None of these

Question 234

The unit of moment of inertia of an area is

A. kg-m2
B. kg-m-s2
C. kg/m2
D. m4

Question 235

The unit of work or energy in S.I. units is

A. Newton
B. Pascal
C. Watt
D. Joule

Question 236

The centre of gravity a T-section 100 mm × 150 mm × 50 mm from its bottom is

A. 50 mm
B. 75 mm
C. 87.5 mm
D. 125 mm

Question 237

The overturning of a vehicle on a level circular path can be avoided if the velocity of vehicle is __________ √(gra/h)

A. Less than
B. Greater than
C. Equal to
D. None of these

Question 238

The moment of inertia of a thin spherical shell of mass m and radius r, about its diameter is

A. mr²/3
B. 2mr²/3
C. 2mr²/5
D. 3mr²/5

Question 239

The efficiency of a screw jack is maximum, when (where α = Helix angle, and φ = Angle of friction.)

A. α = 45° + φ/2
B. α = 45° - φ/2
C. α = 90° + φ
D. α = 90° - φ

Question 240

Efficiency of a screw jack is given by (where α = Helix angle, and φ = Angle of friction.)

A. tan(α + φ)/tanα
B. tanα/tan (α + φ)
C. tan(α - φ)/tanα
D. None of these

Question 241

A differential pulley block has larger and smaller diameters of 100 mm and 80 mm respectively. Its velocity ratio is

A. 5
B. 10
C. 20
D. 40

Question 242

In a screw jack, the effort required to lift the load is given by (where W = Load lifted, α = Helix angle, and φ = Angle of friction.)

A. P = W tan (α - φ)
B. P = W tan (α + φ)
C. P = W tan (φ - α)
D. P = W cos (α + φ)

Question 243

In order to double the period of simple pendulum, the length of the string should be

A. Halved
B. Doubled
D. None of these

Question 244

Joule is the unit of

A. Force
B. Work
C. Power
D. Velocity

Question 245

The impact between two lead spheres is approximately equal to an __________ impact.

A. Elastic
B. Inelastic
C. Solid
D. None of these

Question 246

When trying to turn a key into a lock, following is applied

A. Coplanar force
B. Non-coplanar forces
C. Moment
D. Couple

Question 247

The matter contained in a body, is called

A. Impulsive force
B. Mass
C. Weight
D. Momentum

Question 248

Kinetic friction is the

A. Tangent of angle between normal reaction and the resultant of normal reaction and the limiting friction
B. Ratio of limiting friction and normal reaction
C. The friction force acting when the body is just about to move
D. The friction force acting when the body is in motion

Question 249

The maximum efficiency of a screw jack is

A. (1 - sinφ)/(1 + sinφ)
B. (1 + sinφ)/(1 - sinφ)
C. (1 - tanφ)/(1 + tanφ)
D. (1 + tanφ)/(1 - tanφ)

Question 250

Two non-collinear parallel equal forces acting in opposite direction

A. Balance each other
B. Constitute a moment
C. Constitute a couple
D. Constitute a moment of couple

Question 251

Moment of inertia is the

A. Second moment of force
B. Second moment of area
C. Second moment of mass
D. All of these

Question 252

The total motion possessed by a body, is called

A. Impulsive force
B. Mass
C. Weight
D. Momentum

Question 253

The maximum acceleration of a particle moving with simple harmonic motion is

A. ω
B. ωr
C. ω²r
D. ω/r

Question 254

A semicircular disc rests on a horizontal surface with its top flat surface horizontal and circular portion touching down. The coefficient of friction between semi circular disc and horizontal surface is µ. This disc is to be pulled by a horizontal force applied at one edge and it always remains horizontal. When the disc is about to start moving, its top horizontal force will

A. Remain horizontal
B. Slant up towards direction of pull
C. Slant down towards direction of pull
D. None of the above

Question 255

When a person, on a bicycle, drives round a curve, he has to lean __________ to maintain equilibrium.

A. Inward
B. Outward
C. Towards front
D. Towards back

Question 256

Varingon's theorem of moments states that if a number of coplanar forces acting on a particle are in equilibrium, then

A. Their algebraic sum is zero
B. Their lines of action are at equal distances
C. The algebraic sum of their moments about any point in their plane is zero
D. The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point

Question 257

According to the law of moments, if a number of coplanar forces acting on a particle are in equilibrium, then

A. Their algebraic sum is zero
B. Their lines of action are at equal distances
C. The algebraic sum of their moments about any point in their plane is zero
D. The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point

Question 258

The necessary condition for forces to be in equilibrium is that these should be

A. Coplanar
B. Meet at one point
C. Both (A) and (B) above
D. All be equal

Question 259

The acceleration of a particle moving with simple harmonic motion is __________ at the mean position.

A. Zero
B. Minimum
C. Maximum
D. None of these

Question 260

The motion of a particle round a fixed axis is

A. Translatory
B. Rotary
C. Circular
D. Translatory as well as rotary

Question 261

If a rigid body is in equilibrium under the action of three forces, then

A. These forces are equal
B. The lines of action of these forces meet in a point
C. The lines of action of these forces are parallel
D. Both (B) and (C) above

Question 262

If a number of forces act simultaneously on a particle, it is possible

A. Not a replace them by a single force
B. To replace them by a single force
C. To replace them by a single force through C.G.
D. To replace them by a couple

Question 263

A rubber ball is dropped from a height of 2 m. If there is no loss of velocity after rebounding, the ball will rise to a height of

A. 1 m
B. 2 m
C. 3 m
D. 4 m

Question 264

The centre of percussion of the homogeneous rod of length ‘L’ suspended at the top will be

A. L/2
B. L/3
C. 3L/4
D. 2L/3

Question 265

The units of moment of inertia of mass are

A. kg-m²
B. m²/kg
C. kg/m²
D. kg/m

Question 266

Mass moment of inertia of a uniform thin rod of mass M and length (l) about its mid-point and perpendicular to its length is

A. (2/3) Ml²
B. (1/3) Ml²
C. (3/4) Ml²
D. (1/12) Ml²

Question 267

Forces are called concurrent when their lines of action meet in

A. One point
B. Two points
C. Plane
D. Perpendicular planes

Question 268

The forces, which meet at one point and their lines of action also lie on the same plane, are known as

A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Non-coplanar concurrent forces
D. Non-coplanar non-concurrent forces

Question 269

If u₁ and u₂ are the velocities of two moving bodies in the same direction before impact and v₁ and v₂ are their velocities after impact, then coefficient of restitution is given by

A. (v₁ - v₂)/(u₁ - u₂)
B. (v₂ - v₁)/(u₁ - u₂)
C. (u₁ - u₂)/(v₁ - v₂)
D. (u₂ + u₁)/(v₂ + v₁)

Question 270

A body of mass ‘m’ moving with a constant velocity ‘v’ strikes another body of same mass moving with same velocity but in opposite direction. The common velocity of both the bodies after collision is

A. v
B. 2v
C. 4v
D. 8v

Question 271

A spherical body is symmetrical about its perpendicular axis. According to Routh's rule, the moment of inertia of a body about an axis passing through its centre of gravity is (where, M = Mass of the body, and S = Sum of the squares of the two semi-axes.)

A. MS/3
B. MS/4
C. MS/5
D. None of these

Question 272

Which of the following is not the unit of pressure?

A. kg/cm
B. Bar
C. Atmosphere
D. Newton

Question 273

The velocity of a particle moving with simple harmonic motion is _________ at the mean position.

A. Zero
B. Minimum
C. Maximum
D. None of these

Question 274

The time of flight (t) of a projectile on an upward inclined plane is(where u = Velocity of projection, α = Angle of projection, and β = Inclination of the plane with the horizontal.)

A. t = g cos β/2u sin (α - β)
B. t = 2u sin (α - β)/g cos β
C. t = g cos β/2u sin (α + β)
D. t = 2u sin (α + β)/g cos β

Question 275

One joule is equal to

A. 0.1 N-m
B. 1 N-m
C. 10 N-m
D. 100 N-m

Question 276

One joule means that

A. Work is done by a force of 1 N when it displaces a body through 1 m
B. Work is done by a force of 1 kg when it displaces a body through 1 m
C. Work is done by a force of 1 dyne when it displaces a body through 1 cm
D. Work is done by a force of 1 g when it displaces a body through 1 cm

Question 277

One kg force is equal to

A. 7.8 N
B. 8.9 N
C. 9.8 N
D. 12 N

Question 278

If a body is acted upon by a number of coplanar non-concurrent forces, it may

A. Rotate about itself without moving
B. Move in any one direction rotating about itself
C. Be completely at rest
D. All of these

Question 279

The rate of change of momentum is directly proportional to the impressed force, and takes place in the same direction in which the force acts. This statement is known as

A. Newton's first law of motion
B. Newton's second law of motion
C. Newton's third law of motion
D. None of these

Question 280

When a body falls freely under gravitational force, it possesses __________ weight.

A. No
B. Minimum
C. Maximum
D. None of these

Question 281

The resultant of two forces P and Q acting at an angle θ is

A. √(P² + Q² + 2PQ sinθ)
B. √(P² + Q² + 2PQ cosθ)
C. √(P² + Q² - 2PQ cosθ)
D. √(P² + Q² - 2PQ tanθ)

Question 282

The total energy possessed by a system of moving bodies

A. Is constant at every instant
B. Varies from point to point
C. Is maximum in the start and minimum at the end
D. Is minimum in the start and maximum at the end

Question 283

The forces which do not meet at one point and their lines of action do not lie on the same plane are known as

A. Coplanar concurrent forces
B. Coplanar non-concurrent forces
C. Non-coplanar concurrent forces
D. None of these

Question 284

Which of the following is not the unit of work, energy and heat?

A. kcal
B. kg-m
C. kW-hr
D. h.p

Question 285

The angle which an inclined plane makes with the horizontal when a body placed on it is about to move down is known as angle of

A. Friction
B. Limiting friction
C. Repose
D. Kinematic friction

Question 286

The algebraic sum of moments of the forces forming couple about any point in their plane is

A. Equal to the moment of the couple
B. Constant
C. Both of above are correct
D. Both of above are wrong

Question 287

The force applied on a body of mass 100 kg to produce an acceleration of 5 m/s2, is

A. 20 N
B. 100 N
C. 500 N
D. None of these

Question 288

The periodic time of a particle with simple harmonic motion is _________ proportional to the angular velocity.

A. Directly
B. Inversely
C. Square root
D. None of these

Question 289

The moment of inertia of a square of side a about its diagonal is

A. a²/8
B. a³/12
C. a⁴/12
D. a⁴/16

Question 290

The moment of inertia of a solid cone of mass ‘m’ and base radius ‘r’ about its vertical axis is

A. 3mr²/5
B. 3mr²/10
C. 2mr²/5
D. 4mr²/5

Question 291

A redundant frame is also called __________ frame.

A. Perfect
B. Imperfect
C. Deficient
D. None of these

Question 292

The horizontal range of a projectile (R) is given by

A. R = u² cos2α/g
B. R = u² sin2α/g
C. R = u² cosα/g
D. R = u² sinα/g

Question 293

If the body falls freely under gravity, then the gravitational acceleration is taken as

A. +8.9 m/s2
B. -8.9 m/s2
C. +9.8 m/s2
D. -9.8 m/s2

Question 294

The velocity ratio of a single purchase crab winch can be increased by

A. Increasing the length of the handle
C. Increasing the number of teeth of the pinion
D. All of the above

Question 295

Concurrent forces are those forces whose lines of action

A. Lie on the same line
B. Meet at one point
C. Meet on the same plane
D. None of these

Question 296

A sample of metal weighs 219 gms in air, 180 gms in water, 120 gms in an unknown fluid. Then which is correct statement about density of metal

A. Density of metal can't be determined
B. Metal is twice as dense as water
C. Metal will float in water
D. Metal is twice as dense as unknown fluid

Question 297

The center of percussion of a solid cylinder of radius ‘r’ resting on a horizontal plane will be

A. r/2
B. 2r/3
C. r/A
D. 3r/2

Question 298

The magnitude of two forces, which when acting at right angle produce resultant force of VlOkg and when acting at 60° produce resultant of Vl3 kg. These forces are

A. 2 and V6
B. 3 and 1 kg
C. V5andV5
D. 2 and 5

Question 299

The ratio of static friction to dynamic friction is always

A. Equal to one
B. Less than one
C. Greater than one
D. None of these

Question 300

If a suspended body is struck at the center of percussion, then the pressure on die axis passing through the point of suspension will be

A. Maximum
B. Minimum
C. Zero
D. Infinity

Question 301

Which of the following statement is correct in connection with projectiles?

A. A path, traced by a projectile in the space, is known as trajectory.
B. The velocity, with which a projectile is projected, is known as the velocity of projection.
C. The angle, with the horizontal, at which a projectile is projected, is known as angle of projection.
D. All of the above

Question 302

The periodic time of one oscillation for a simple pendulum is (where l = Length of the pendulum.)

A. (1/2π). √(l/g)
B. (1/2π). √(g/l)
C. 2π. √(l/g)
D. None of these

Question 303

The velocity ratio for the first system of pulleys is (where n is the number of pulleys.)

A. n
B. n²
C. 2n
D. 2n - 1

Question 304

Static friction is always __________ dynamic friction.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 305

The center of gravity of a quadrant of a circle lies along its central radius (r) at a distance of

A. 0.5 r
B. 0.6 r
C. 0.7 r
D. 0.8 r

Question 306

The C.G. of a plane lamina will not be at its geometrical centre in the case of a

A. Right angled triangle
B. Equilateral triangle
C. Square
D. Circle

Question 307

A framed structure is imperfect, if the numbers of members are __________ (2j - 3).

A. Equal to
B. Less than
C. Greater than
D. Either (B) or (C)

Question 308

The units of moment of inertia of an area are

A. kg-m²
B. m⁴
C. kg/m²
D. m³

Question 309

Which of the following are vector quantities?

A. Linear displacement
B. Linear velocity
C. Linear acceleration
D. All of these

Question 310

Which of the following are vector quantities?

A. Angular displacement
B. Angular velocity
C. Angular acceleration
D. All of these

Question 311

The C.G. of a right circular solid cone of height h lies at the following distance from the base

A. h/2
B. J/3
C. h/6
D. h/4

Question 312

When a body of mass 'm' attains a velocity 'v' from rest in time 't', then the kinetic energy of translation is

A. mv2
B. mgv2
C. 0.5 mv2
D. 0.5 mgv2

Question 313

If two bodies having masses m1 and m2 (m1>m2) have equal kinetic energies, the momentum of body having mass m1 is _________ the momentum of body having mass m2.

A. Equal to
B. Less than
C. Greater than
D. None of these

Question 314

Three forces acting on a rigid body are represented in magnitude, direction and line of action by the three sides of a triangle taken in order. The forces are equivalent to a couple whose moment is equal to

A. Area of the triangle
B. Twice the area of the triangle
C. Half the area of the triangle
D. None of these

Question 315

The M.I. of hollow circular section about a central axis perpendicular to section as compared to its M.I. about horizontal axis is

A. Same
B. Double
C. Half
D. Four times

Question 316

A weight of 1000 N can be lifted by an effort of 80 N. If the velocity ratio is 20, the machine is

A. Reversible
B. Non-reversible
C. Ideal
D. None of these

Question 317

A ladder is resting on a rough ground and leaning against a smooth vertical wall. The force of friction will act

A. Downward at its upper end
B. Upward at its upper end
C. Zero at its upper end
D. Perpendicular to the wall at its upper end

Question 318

A ladder is resting on a smooth ground and leaning against a rough vertical wall. The force of friction will act

A. Towards the wall at its upper end
B. Away from the wall at its upper end
C. Downward at its upper end
D. Upward at its upper end

Question 319

The moment of inertia of a rectangular section 3 cm wide and 4 cm deep about X-X axis is

A. 9 cm4
B. 12 cm4
C. 16 cm4
D. 20 cm4

Question 320

The product of either force of couple with the arm of the couple is called

A. Resultant couple
B. Moment of the forces
C. Resulting couple
D. Moment of the couple

Question 321

The resolved part of the resultant of two forces inclined at an angle 'θ' in a given direction is equal to

A. The algebraic sum of the resolved parts of the forces in the given direction
B. The sum of the resolved parts of the forces in the given direction
C. The difference of the forces multiplied by the cosine of θ
D. The sum of the forces multiplied by the sine of θ

Question 322

One end of a helical spring is fixed while the other end carries the load W which moves with simple harmonic motion. The frequency of motion is given by (where δ = Deflection of the spring.)

A. 2π. √(g/δ)
B. 1/2π. √(g/δ)
C. 2π. √(δ/g)
D. 1/2π. √(δ/g)

Question 323

The moment of inertia of a sphere of mass 'm' and radius 'r', about an axis tangential to it, is

A. 2mr²/3
B. 2mr²/5
C. 7mr²/3
D. 7mr²/5

Question 324

The range of projectile will be maximum for a given velocity of projectile, when the angle of projection (α) is

A. β/2
B. 30° + β/2
C. 45° + β/2
D. 60° + β/2

Question 325

Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its C.G. and parallel to the depth (d), is

A. db³/12
B. bd³/12
C. db³/36
D. bd³/36

Question 326

Moment of inertia of a rectangular section having width (b) and depth (d) about an axis passing through its C.G. and parallel to the width (b), is

A. db³/12
B. bd³/12
C. db³/36
D. bd³/36