1. 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
2. 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 the above
3. 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
4. The unit of force in S.I. system of units is
(a) dyne (b) kilogram
(c) newton (d) watt
5. One kg force is equal to
(a) 7.8 N (b) 8.9 N
(c) 9.8 N (d) 12 N
6. 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
7. The process of finding out the resultant force is
called.......... of forces.
(a) composition (b) resolution
8. 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 the above
9. Vectors method for the resultant force is also called
polygon law of forces.
(a) Correct (b) Incorrect
10. The resultant of two forces P and Q acting at an angle T is
(a) 2 2 P Q PQ T 2 sin
(b) 2 2 P Q PQ 2 cos T
(c) 2 2 P Q PQ – 2 cos T
(d) 2 2 P Q PQ – 2 tan T
11. If the resultant of two forces P and Q acting at an
angleT, makes an angle D with the force P, then
(a) tan D = sin cos P P Q T T
(b) tan D = cos cos P P Q T T
(c) tan D = sin cos Q P Q T T
(d) tan D = cos sin Q P Q T T
12. 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
13. The resultant of two equal forces P making an angle
T, is given by
(a) 2 sin / 2 P T (b) 2 cos / 2 P T
(c) 2 tan / 2 P T (d) 2 cot / 2 P T
14. The resultant of two forces each equal to P and acting
at right angles is
(a) P / 2 (b) P / 2
(c) P /2 2 (d) 2 P
15. The angle between two forces when the resultant is
maximum and minimum respectively are
(a) 0o and 180o (b) 180o and 0o
(c) 90o and 180o (d) 90o and 0o
16. 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) 30o (b) 60o
(c) 90o (d) 120o
17. 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
18. Two forces are acting at an angle of 120o.The bigger
force is 40N and the resultant is perpendicular to the
smaller one. The smaller force is
(a) 20 N (b) 40 N
(c) 80 N (d) none of these
19. Four forces P, 2P, 3P and 4P act along the sides taken
in order of a square. The resultant force is
(a) 0 (b) 2 2P
(c) 2 P (d) 5P
20. The terms ‘leverage’ and ‘mechanical advantage’ of
a compound lever have got the same meaning.
(a) Right (b) Wrong
21. 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. 6V = 0)
(d) sum of resolved parts in the horizontal direction
is zero (i.e. 6H = 0)
22. If a number of forces are acting at a point, their
resultant is given by
(a) (6V)2+ (6H)2
(b) 2 2 ()( ) 6 6 V H
(c) 2 2 ( ) ( ) 2( )( ) 6 6 6 6 V H VH
(d) 2 2 ( ) ( ) 2( )( ) 6 6 6 6 V H VH
23. Fig. 1.41 shows the two equal
forces at right angles acting at
a point. The value of force R
acting along their bisector and in
opposite direction is
(a) P / 2 (b) 2 P
(c) 2 P (d) P / 2
24. If a number of forces are acting at a point, their
resultant will be inclined at an angle T with the
horizontal, such that
(a) tan / T 6 6 H V (b) tan / T 6 6 V H
(c) tan T 6 u6 V H (c) tan T 6 6 V H
25. 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
26. The polygon law of forces states that if a number
of forces, acting simultaneously on a particle, be
represented in magnitude and direction by the sides
a polygon taken in order, then their resultant is
represented in magnitude and direction by the closing
side of the polygon, taken in opposite direction.
(a) Correct (b) Incorrect
27. 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 the above
28. Which of the following condition(s) is/are valid for
the equilibrium of a rigid body subjected to three
coplanar forces?
(a) All forces are parallel
(b) All forces are concurrent
(c) At least two forces are concurrent
(d) all of the above
29. If the resultant of a number of forces acting on a body
is zero, then the body will not be in equilibrium.
(a) Yes (b) No
30. 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
31. The forces, which do not meet at one point, but their
lines of action lie on the same plane, are known as
coplanar non-concurrent forces.
(a) Agree (b) Disagree
32. 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
33. 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 the above
34. 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
35. 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
36. 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
37. 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
38. If three coplanar forces acting on a point are in
equilibrium, then each force is proportional to the
sine of the angle between the other two.
(a) Right (b) Wrong
39. Fig. 1.42 shows the three coplanar forces P, Q and R
acting at a point O. If these forces are in equilibrium,
then
(a) sin sin sin
PQR EDJ
(b) sin sin sin
PQR DEJ
(c) sin sin sin
PQR JDE
(d) sin sin sin
PQR DJE
40. According to lami’s theorem
(a) the three forces must be equal
(b) the three forces must be at 120o 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
41. 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
42. If three forces acting at a point are represented
in magnitude and direction by the three sides of
a triangle, taken in order, then the forces are in
equilibrium.
(a) Yes (b) No
43. If a number of forces acting at a point be represented
in magnitude and direction by the three sides of a
triangle, taken in order, then the forces are not in
equilibrium.
(a) Agree (b) Disagree
44. 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 traingle, 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
45. The moment of the force P about O as shown in Fig.
1.43, is
(a) P × OA (b) P × OB
(c) P × OC (d) P × AC
46. 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
47. Varignon’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.
48. 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.
49. 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
50. 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
51. 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
52. Two like parallel forces are acting at a distance of
24 mm apart and their resultant is 20 N. If 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
53. 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 the above
54. A smooth cylinder lying on its convex surface remains
in .......... equilibrium.
(a) stable (b) unstable
(c) neutral
55. 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 the above
56. 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 centre of gravity of the
body
(d) maximum, if it acts at the centre of gravity of the
body
57. A smooth cylinder lying on a .......... is in neutral
equilibrium.
(a) curved surface
(b) convex surface
(c) horizontal surface
58. If three forces acting at a point be represented in
magnitude and direction by the three sides of a triangle,
taken in order, the forces shall be in equilibrium.
(a) True (b) False
59. Two equal and opposite parallel forces whose lines
of action are different, can be replaced by a single
force parallel to the given forces.
(a) Correct (b) Incorrect
60. Two equal and opposite parallel forces whose lines
of action are different form a couple.
(a) Right (b) Wrong
61. A couple consists of two
(a) unlike parallel forces of different magnitude
(b) like parallel forces of different magnitude
(c) like parallel forces of same magnitude
(d) unlike parallel forces of same magnitude
62. A couple produces
(a) translatory motion
(b) rotational motion
(c) combined translatory and rotational motion
(d) none of the above
63. 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
64. A coplanar force and a coplanar couple acting on a
rigid body
(a) balance each other
(b) cannot balance each other
(c) produce moment of a couple
(d) produce force and couple
65. Match the correct answer from Group B for the
statements given in Group A.
Group A Group B
(a) The resultant of two forces
P and Q (P > Q) acting
along the same straight
line, but in opposite
direction, is
(A) P + Q
(b) The resultant of two like
parallel forces, P and Q, is
(B) P – Q
(c) The resultant of two equal forces P making an angle T, is
(C) sin cos Q P Q T T
(d) The angle of inclination
of the resultant of the two
forces P and Q, with the
force P, is
(D) 2 cos 2 P T
66. The force induced in the string
AB due to the load W, as shown
in Fig. 1.44, is
(a) W sin T
(b) W cos T
(c) W sec T
(d) W cosec T
67. The force induced in the string BC due to the load
W as shown in Fig. 1.44, is
(a) W sin T (b) W cos T
(c) W tan T (d) W cot T
68. A couple can be balanced by
(a) a force (b) a moment
(c) a torque
(d) an equal and opposite couple
69. The point, through which the whole weight of the
body acts, irrespective of its position, is known as
(a) moment of inertia (b) centre of gravity
(c) centre of percussion (d) centre of mass
70. 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
71. An irregular body may have more than one centre of
gravity.
(a) Yes (b) No
72. The centre of gravity of a rectangle lies at a point
where its two diagonals meet each other.
(a) Agree (b) Disagree
73. The centre of gravity of a triangle lies at a point where
its medians intersect each other.
(a) True (b) False
74. The centre of gravity of an isosceles triangle with
base ( p) and sides (q) from its base is
(a)
2 2 4 –
6
p q (b)
2 2 4 –
6
p q
(c)
2 2 –
4
p q (d)
2 2
4
p q
75. The centre of gravity of an equilateral triangle with
each side a, is..............from any of the three sides.
(a) 3 a / 2 (b) 23 a
(c) a / 2 3 (d) 32 a
76. The centre of gravity of a semi-circle lies at a distance
of..............from its base measured along the vertical
radius.
(a) 3r / 8 (b) 4r / 3S
(c) 8r / 3 (d) 3r / 4S
77. The centre of gravity of a hemisphere lies at a distance
of 3r / 8 from its base measured along the vertical
radius.
(a) Right (b) Wrong
78. The centre of gravity of a
trapezium with parallel sides
a and b lies at a distance of y
from the base b, as shown in
Fig. 1.45. The value of y is
(a)
2a b h
a b
§ · ̈ ̧ © 1 (b)
2
2
h ab
a b
§ · ̈ ̧ © 1
(c)
2
3
h ab
a b
§ · ̈ ̧ © 1 (d) 3 2
h ab
a b
§ · ̈ ̧ © 1
79. The centre of gravity of a right circular solid cone is
at a distance of...........from its base, measured along
the vertical axis.
(a) h / 2 (b) h / 3
(c) h / 4 (d) h / 6
where h = Height of a right circular solid cone.
80. The perpendicular distance between the diameter of
a semi-circular area to its centroid is given by
(a) 3r / 8S (b) 4r / 3S
(c) 3r / 4S (d) 5r / 4S
81. The centre of gravity of a right angled triangle lies at
its geometrical centre.
(a) Correct (b) Incorrect
82. Match the correct answer from Group B for the
statements given in Group A.
Group A Group B
(a) C.G. of a rectangle (A) is at its centre
(b) C.G. of a triangle (B) is at intersection
of its diagonals
(c) C.G. of a circle (C) is at 4r/3Sfrom
its base along the
vertical radius
(d) C.G. of a semicircle (D) is at h/4 from its
base along the
vertical axis
(e) C.G. of a hemisphere (E) is at intersection of
its medians
( f) C.G. of a right
circular cone
(F) is at 3r / 8 from
its base along the
vertical radius
83. The centre 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
84. 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
85. A circular hole of 50 mm diameter
is cut out from a circular disc of
100 mm diameter as shown in
Fig. 1.46. The centre of gravity
of the section will lie
(a) in the shaded area
(b) in the hole
(c) at O
86. Moment of inertia is the
(a) second moment of force
(b) second moment of area
(c) second moment of mass
(d) all of the above
87. The unit of moment of inertia of an area is
(a) kg-m2
(b) kg-m-s2
(c) kg / m2
(d) m4
88. The unit of mass moment of inertia in S.I. units is kg - m2.
(a) True (b) False
89. 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
(a) 3/MS
(b) 4
(c) 5
MS (d) none of these
where M = Mass of the body, and
S = Sum of the squares of the two semi-
axes.
90. The radius of gyration is the distance where the
whole mass (or area) of a body is assumed to be
concentrated.
(a) Correct (b) Incorrect
91. 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
M l2
(c)
3
4
Ml2 (d)
4
3
Ml2
92. 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
93. 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)
3
12
db (b)
3
12
bd
(c)
3
36
db (d)
3
36
bd
94. 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)
3
12
db (b)
3
12
bd
(c)
3
36
db (d)
3
36
bd
95. The moment of inertia of a square of side (a) about
an axis through its centre of gravity is
(a) a
4 / 4 (b) a
4 / 8
(c) a
4 / 12 (d) a
4 / 36
96. The moment of inertia of a rectangular section 3cm
wide and 4cm deep about X–X axis is
(a) 9 cm4 (b) 12 cm4
(c) 16 cm4 (d) 20 cm4
97. The moment of inertia of a square of side a about its
base is a
4 / 3.
(a) True (b) False
98. The moment of inertia of a square of side a about its
diagonal is
(a) a
2 / 8 (b) a
3 / 12
(c) a
4 / 12 (d) a
4 / 16
99. Moment of inertia of a hollow rectangular section as
shown in Fig. 1.47, about X-X axis, is
(a)
3 3
– 12 12
BD bd
(b)
3 3
– 12 12
DB db
(c)
3 3
– 36 36
BD bd
(d)
3 3
– 36 36
DB db
100. Moment of inertia of a hollow rectangular section as
shown Fig. 1.47, about Y-Y axis, is not the same as
that about X-X axis.
(a) Yes (b) No
101. Moment of inertia of a circular section about its
diameter (d) is
(a) S d 3 / 16 (b) S d 3 / 32
(c) S d 4 / 32 (d) S d 4 / 64
102. Moment of inertia of a circular section about an axis
perpendicular to the section is
(a) S d 3 / 16 (b) S d 3 / 32
(c) S d 4 / 32 (d) S d 4 / 64
103. Moment of inertia of a hollow circular section, as
shown in Fig. 1.48, about X-X axis, is
(a) 2 2 ( –) 16
D d S
(b) 3 3 ( –) 16
D d S
(c) 4 4 ( –) 32
D d S
(d) 4 4 ( –) 64
D d S
104. Moment of inertia of a hollow circular section, as
shown in Fig. 1.48, about an axis perpendicular to
the section, is........... than that about X-X axis.
(a) two times (b) four times
(c) one-half
105. 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
106. 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
107. 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.
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