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 force d) all of these
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 these
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 b) 8.9N c) 9.8N d) 12N
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 these
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 θ is
a) √𝑃2 + 𝑄2 + 2𝑃𝑄𝑠𝑖𝑛𝜃 b) √𝑃2 + 𝑄2 + 2𝑃𝑄𝑐𝑜𝑠𝜃
c) √𝑃2 + 𝑄2 − 2𝑃𝑄𝑐𝑜𝑠𝜃 d) √𝑃2 + 𝑄2 − 2𝑃𝑄𝑡𝑎𝑛𝜃
11. If the resultant of two forces P and Q acting at an angle θ, makes an angle with the force P,
then
a) tan =
𝑃 𝑠𝑖𝑛𝜃
𝑃+𝑄 𝑐𝑜𝑠𝜃 b) tan 𝑎 =
𝑃 𝑐𝑜𝑠𝜃
𝑃 +𝑄 𝑐𝑜𝑠𝜃
c) tan 𝛼 =
𝑄 sin 𝜃
𝑃+𝑄 𝑐𝑜𝑠𝜃 d) tan 𝛼 =
𝑄 𝑐𝑜𝑠𝜃
𝑃+𝑄 𝑠𝑖𝑛𝜃
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 θ, is given by
a) 2 P sin θ/2 b) 2 P cos θ/2 c) 2 P tan θ/2 d) 2 P cot θ/2
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) 0° and 180° b) 180° and 0° c) 90° and 180° d) 90° and 0°
16. If the resultant of two equal forces has the same magnitude as dither of the forces, then the
angle between the two forces is
a) 30° b) 60° c) 90° d) 120°
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 resultant of the two forces P and Q is R. If Q is doubled, the new resultant is perpendicular
to P, then
a) 20N b) 40N c) 80 N d) none of these
19. The term ‘leverage’ and ‘mechanical advantage’ of a compound lever have got the same
meaning
a) Right b) Wrong
20. 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) sum of resolved parts in the horizontal direction is zero ( i.e. ∑H = 0 )
21. 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)
22. Fig. show the two equal forces at right angles acting at a point. The value of forces R acting
along their bisector and in opposite direction is
a) P/2 b) 2P
c) √2 P d) P/√2
23. 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 = ∑𝐻/∑𝑉 b) 𝑡𝑎𝑛𝜃 = ∑𝑉/∑𝐻
c) 𝑡𝑎𝑛𝜃 = ∑𝑉 × ∑𝐻 d) 𝑡𝑎𝑛𝜃 = √∑𝑉 + ∑𝐻
24. The triangle law of forces states that if two forces actin 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 directed by the third side of a triangle, taken in
opposite order.
a) True b) False
25. 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
26. 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
27. 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
28. The forces, which meet at one point and their lines of action also lie on the same plane, are
known as
a) coplaner concurrent forces b) coplaner non-concurrent forces
B) non-coplaner concurrent forces non-coplaner non-concurrent forces
29. The forces, which do not meet at one point, but their lines of action lie on the same plane, are
known as coplaner concurrent forces.
a) Agree b) Disagree
30. The forces which meet at one point, but their lines of action………. on the same plane, are
known as non-coplaner concurrent forces.
a) lie b) do not lie
31. 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) coplaner concurrent forces b) coplaner non-concurrent forces
c) non-coplaner concurrent forces d) none of these
32. Coplaner 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
33. Coplaner 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 o 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
34. Non-coplaner 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
35. Non-coplaner non-noncurrent 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
36. If three coplaner forces acting on a point are in equilibrium, then each force is proportional to
the line of the angle between the other two.
a) Right b) Wrong
37. Fig. shows the three coplaner forces P,Q and R acting at a point P, if these forces are in
equilibrium, then
a)
𝑃
𝑠𝑖𝑛𝛽
=
𝑄
𝑠𝑖𝑛𝛼
=
𝑅
𝑠𝑖𝑛𝛾
b)
𝑃
𝑠𝑖𝑛𝛼
=
𝑄
𝑠𝑖𝑛𝛽
=
𝑅
𝑠𝑖𝑛𝛾
c) 𝑃
𝑠𝑖𝑛𝛾
=
𝑞
𝑠𝑖𝑛𝛼
=
𝑅
𝑠𝑖𝑛𝛽
d) 𝑃
𝑠𝑖𝑛𝛼
=
𝑄
𝑠𝑖𝑛𝛾
=
𝑅
𝑠𝑖𝑛𝛽
38. 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 forces is proportional to the
sine of the angle between the other two
39. If a given force ( or a given system of forces ) acting on a body………………... the position of the
body, but deeps it in equilibrium, then its effect is to produce internal stress in the body.
a) change b) does not change
40. If a number of 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
41. 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
42. 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 tringle, 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
43. The moment of the force P about O as shown in fig. is
a) P x OA b) P x OB
c) P x OC d) P x AC
44. If a number of coplaner 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
45. Varingon’s theorem of moments states that if a number of coplaner 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 is equal to the moment of their
resultant force about the same point.
d) the algebraic sum of their moments about any point is equal to the moment of their
resultant force about the same point.
46. According to the law of moments, if a number of coplaner 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
forcea about the same point.
47. For any system of coplaner 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
48. The forces, whose lines of action are parallel to each other and act in the same directions, are
known as
a) coplaner concurrent forces b) coplaner non-concurrent forces
c) like parallel forces d) unlike parallel forces
49. The three forces for 100N, 200N, and 300N have their lines of action parallel to each other but
act in the opposite directions. These forces are known as
a) coplaner concurrent forces b) coplaner non-concurrent force
c) like parallel forces d) unlike parallel forces
50. Two like parallel forces are acting at a distance of 24 mm apart and their resultant is 20N. If the
line of action of the resultant is 6mm from any given force, the two force are
a) 15 N and 5 N b) 20 N and 5 N c) 15 N and 15 N d) none
51. If a body is acted upon by a number of coplaner 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
52. A smooth cylinder lying on its convex surface remains in ………. Equilibrium.
a) stable b) unstable c) neutral
53. 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
54. 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
55. A smooth cylinder cylinder lying on a ………… is in neutral equilibrium.
a) curved surface b) convex surface c) horizontal surface
56. 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
57. Two equal and opposite parallel forces whose lines of action are different, can be replaced by
single force parallel to the given forces.
a) Correct b) Incorrect
58. Two equal and opposite parallel forces whose lines of action are different form a couple.
a) Right b) Wrong
59. A couple produces
a) translatory motion b) rotational motion
c) combined translatory and rotational motion
d) none of these
60. 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
61. 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
b) The resultant of two like parallel
forces, P and Q, is
c) The resultant of two equal forces P
making an angle θ, is
d) The angle of inclination of the
resultant of the two forces p and Q,
with the force P, is
A) P + Q
B) P – Q
C) 𝑄 𝑠𝑖𝑛𝜃
𝑃+𝑄 𝑐𝑜𝑠𝜃
D) 2𝑃 𝐶𝑂𝑆 𝜃
2
62. The following induced in the string AB due to the load W, as shown in figure, is
a) 𝑊 𝑠𝑖𝑛𝜃 b) 𝑊 𝑐𝑜𝑠𝜃
c) 𝑊 𝑠𝑒𝑐𝜃 d) 𝑊 𝑐𝑜𝑠𝑒𝑐
63. The force induced in the string BC due to the load W as shown in figure, is
a) 𝑊 𝑠𝑖𝑛𝜃 b) 𝑊 𝑐𝑜𝑠𝜃
c) 𝑊 𝑡𝑎𝑛𝜃 d) 𝑊 𝑐𝑜𝑡𝜃
64. 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 gravity d) centre of mass
65. 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
66. An irregular body may have more than one centre of gravity.
a) Yes b) No
67. The centre of gravity of a rectangular lies at a point where its two diagonals meet each other.
a) Agree b) Disagree
68. The centre of gravity of a triangle lies at a point where its medians intersect each other.
a) True b) False
69. The centre of gravity of an isosceles triangle with base (p) and sides (q) from its base is
a) √4𝑝2−𝑞2
6
b) 4𝑝
2−𝑞
2
6
c ) 𝑝
2−𝑞
2
4
d) 𝑝
2+𝑞
2
4
70. The centre of gravity of an equilateral triangle with each side s, is …………from any of the three
sides.
a) √3 a / 2 b) 2√3 a c) a √2 √3 d) 3 √2 a
71. 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 / 3π c) 8r / 3 d) 3r / 4π
72. 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
73. 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 figure. The value of y is
a) ℎ (
2𝑎+𝑏
𝑎+𝑏
) b) ℎ
2
(
2𝑎+𝑏
𝑎+𝑏
)
c) ℎ
3
(
2𝑎+𝑏
𝑎+𝑏
) d)
ℎ
3
(
𝑎+𝑏
2𝑎+𝑏
)
74. 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
75. The centre of gravity of a right angled triangle lies at its geometrical centre.
a) Correct b) Incorrect
76. Match the correct answer from Group B for the statements given in Group A.
Group A Group B
a) C.G of a rectangle
b) C.G. of a triangle
c) C.G. of a circle
d) C.G. of a semicircle
e) C.G. of a hemisphere
f) C.G. of a right circular cone
A) Is at its centre
B) Is at intersection if its diagonals
C) Is at 4r/ 3π from its base along the
vertical radius
D) Is at h/4 from its base along the
vertical axis
E) Is at intersection of its medians
F) Is at 3r/ 8 from its base along the
vertical radius
77. The centre of gravity of a quadrant of a circle lies along its central radius ® at a distance of
a) 0.5 r b) 0.6 r c) 0.7 r d) 0.8 r
78. The centre of gravity a T-section 100mm x 150mm x 50mm from its bottom is
a) 50mm b) 75mm c) 87.5mm d) 125mm
79. A circular hole of 50 mm diameter is cut out from a circular disc of 100mm diameter as shown
in figure. The centre of gravity of the section will be
a) in the shaded area b) in the hole c) at O
80. Moment of inertia is the
a) second moment of force b) second moment of area
c) second moment of mass d) all of these
81. The unit of moment of inertia of an area is
a) 𝑘𝑔 − 𝑚2 b) 𝑘𝑔 − 𝑚𝑠
2
c) 𝑘𝑔/𝑚2
d) 𝑚2
82. The unit or mass moment of inertia in S.I. units is kg-m2
.
a) True b) False
83. 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) 𝑚𝑠
3
b) 𝑚𝑠
4
c) 𝑚𝑠
5
d) none of these
84. 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
85. 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
𝑀𝐼
2 b) 1
3
𝑀𝐼
2
c) 3
4
𝑀𝐼
2 d) 4
3
𝑀𝐼
2
86. Mass moment of inertia if 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
87. 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) 𝑑𝑏
3
12
b) 𝑏𝑑
3
12
c) 𝑑𝑏
3
36
d) 𝑏𝑑
3
36
88. 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) 𝑑𝑏
3
12
b)
𝑏𝑑
3
12
c) 𝑑𝑏
3
36
d) 𝑏𝑑
3
36
89. The moment of inertia of a square of side ( a ) about an axis through its centre of gravity is
a) a4
/4 b) a4
/8 c) a4
/12 d) a4
/36
90. The moment of inertia of a rectangular section 3cm wide and 4 cm deep about X-X axis is
a) 9cm4 b) 12 cm4
c) 16 cm4 d) 20 cm4
91. The moment of inertia of a square of side a about its base is a
4 /3.
a) True b) False
92. The moment of inertia of a square of side a about its diagonal is
a) a
2
/8 b) a3
/12 c) a4
/12 d) a4 / 16
93. Moment of inertia of a hollow rectangular section as shown in figure, about x-x axis, is
a) 𝐵𝐷
3
12
−
𝑏𝑑
3
12
b)
𝐷𝐵
3
12
−
𝑑𝑏
3
12
c) 𝐵𝐷
3
36
−
𝑏𝑑
3
36
d) 𝐷𝐵
3
36
−
𝑑𝑏
3
36
94. Moment of inertia of a hollow rectangular section as shown in figure, about Y-Y axis, is not the
same as that about X-X axis.
a) Yes b) No
95. Moment of inertia of a circular section about its diameter (d) is
a) 𝜋𝑑
3
/16 b) 𝜋𝑑
3
/32 c) 𝜋𝑑
4
/32 d) 𝜋𝑑
4
/64
96. Moment of inertia of a circular section about an axis perpendicular to the section is
a) 𝜋𝑑
3
/16 b) 𝜋𝑑
3
/32 c) 𝜋𝑑
4
/32 d) 𝜋𝑑
4
/64
97. Moment of inertia of a hollow circular section, as shown fig. about X-X axis, is
a) 𝜋
16
(𝐷
2 − 𝑑
2
) b) 𝜋
16
(𝐷
3 − 𝑑
3
)
c) 𝜋
32
(𝐷
2 − 𝑑
2
) d) 𝜋
32
(𝐷
3 − 𝑑
3
)
98. Moment of inertia of a hollow circular section, as shown in figure about an axis perpendicular to
the section, is …………….than that about X-X axis.
a) two times b) same c) half
99. 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) bh2/4
b) bh3/8
c) bh3/12
d) bh3/36
100. 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
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