61. For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively.
(a) 122.47 kN and 50 kN
(b) 70.71 kN and 100 kN
(c) 70.71 kN and 50 kN
(d) 81.65 kN and 100 kN
(2 Mark, 2015[1])

Ans: c
Explanation:
62. For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is
(a) 10
(b) 14.14
(c) 20
(d) 28.28
(2 Mark, 2015[2])

Ans: c
Explanation:
63. A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be
(1 Mark, 2015[2])

Ans: 8
Explanation:
64. The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following expression: a = − 0.1V, Where, V is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be ____.
(2 Mark, 2015[2])

Ans: 29.6
We know, a=\frac { dv }{ dt } =0.1v
=> \frac { dv }{ v } =0.1t
=> \int _{ 40 }^{ v }{ \frac { dv }{ v } } =\int _{ 0 }^{ 3 }{ 0.1dt }
=> ln v – ln 40 = 0.1 * 3
=> v = 29.6 m/s
65. A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions T_{1} and T_{2} are respectively.
(a) 433 N and 250 N
(b) 250 N and 433 N
(c) 353.5 N and 250 N
(d) 250 N and 353.5 N
(1 Mark, 2015[3])

Ans: a
Explanation:
66. Figure shows a wheel rotating about O_{2}. Two points A and B located along the radius of wheel have speeds of 80 m/s and 140 m/s respectively. The distance between the points A and B is 300 mm. The diameter of the wheel (in mm) is ___.
(2 Mark, 2015[3])

Ans: 1400
Explanation:
67. A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots.
Helical slots are such that one turn of helix is completed over a distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is _____.
(2 Mark, 2015[3])

Ans: 251.3
Explanation:
71. A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of 30^{0} with the vertical. The magnitude of force F (in N) is ____.
(1 Mark, 2016[1])

Ans: 57.7
Explanation:
72. A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is
(a) \sqrt { gH }
(b)\sqrt { 2gR }
(c) \sqrt { 2gH }
(d) 0
(1 Mark, 2016[1])

Ans: c
At initial position,
The potential energy = MgH
At the bottom,
The kinetic energy = \frac { 1 }{ 2 } M{ v }^{ 2 }
According to conservation of energy,
MgH =\frac { 1 }{ 2 } M{ v }^{ 2 }
=> v=\sqrt { 2gH }
73. A block of mass m rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is 0.25. The string can withstand a maximum force of 20 N. The maximum value of the mass (m) for which the string will not break and the block will be in static equilibrium is ____________ kg.
Take cosθ = 0.8 and sinθ = 0.6. Acceleration due to gravity g = 10 m/s^{2}
(2 Mark, 2016[1])

Ans: 5
Explanation:
74. A twomember truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively
(a) 2W tensile and \sqrt { 3 }W compressive
(b) \sqrt { 3 }W tensile and 2W compressive
(c) \sqrt { 3 }W compressive and 2W tensile
(d) 2W compressive and \sqrt { 3 }W tensile
(2 Mark, 2016[1])

Ans: b
Explanation:
75. The figure below represents a triangle PQR with initial coordinates of the vertices as P(1,3), Q(4,5) and R(5,3.5). The triangle is rotated in the XY plane about the vertex P by angle θ in clockwise direction. If sinθ = 0.6 and cosθ = 0.8, the new coordinates of the vertex Q are
(a) (4.6, 2.8)
(b) (3.2, 4.6)
(c) (7.9, 5.5)
(d) (5.5, 7.9)
(2 Mark, 2016[1])

Ans: a
Explanation:
76. A point mass having mass M is moving with a velocity V at an angle θ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is
(a) 2MV cosθ
(b) 2MV sinθ
(c) 2MV cosθ
(d) 2MV sinθ
(1 Mark, 2016[2])

Ans: d
Explanation:
77. For the situation shown in the figure below the expression for H in terms of r, R and D is
(a) 𝐻 = 𝐷 + \sqrt { { r }^{ 2 }{ +R }^{ 2 } }
(b) 𝐻 = (𝑅 + 𝑟) + (𝐷 + 𝑟)
(c) 𝐻 = (𝑅 + 𝑟) +\sqrt { { D }^{ 2 }{ R }^{ 2 } }
(d) 𝐻 = (𝑅 + 𝑟) +\sqrt { 2D(R+r)D^{ 2 } }
(2 Mark, 2016[2])
78. An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is ______.
(2 Mark, 2016[3])

Ans: 133.33
Explanation:
79. A force F is acting on a bent bar which is clamped at one end as shown in the figure
(1 Mark, 2016[3])

Ans: a
Explanation:
80. A circular disc of radius 100 mm and mass 1 kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed v of the disc when it reaches position B is _________ m/s.
Acceleration due to gravity g = 10 m/s^{2}
(2 Mark, 2016[3])

Ans: 20
Explanation:
81. A point P (1, 3, −5) is translated by 2𝑖 + 3𝑗 − 4𝑘 and then rotated counter clockwise by 90^{0} about the zaxis. The new position of the point is
(a) (−6, 3, −9)
(b) (−6, −3, −9)
(c) (6, 3, −9)
(d) (6, 3, 9)
(2 Mark, 2016[3])

Ans: a
Explanation:
82. A rigid rod (AB) of length 𝐿 = 2 m is undergoing translational as well as rotational motion in the xy plane (see the figure). The point A has the velocity 𝑉_{1} = i + 2j m/s. The end B is constrained to move only along the x direction. The magnitude of the velocity V_{2} (in m/s) at the end B is _____.
(2 Mark, 2016[3])

Ans: 3
Given, { V }_{ 1 } = i + 2j
Magnitude of { V }_{ 1 }=\sqrt { { 1 }^{ 2 }+{ 2 }^{ 2 } } =\sqrt { 5 }
Again, \alpha +{ 45 }^{ 0 }={ tan }^{ 1 }\frac { 2 }{ 1 }
=> \alpha =18.434^{ 0 }
Since the rod is rigid, the velocity at point A and B along the rod AB is equal.
{ V }_{ 1 }cos\alpha = { V }_{ 2 }cos{ 45 }^{ 0 }
=> \sqrt { 5 } \times cos{ 18.434 }^{ 0 }={ V }_{ 2 }cos{ 45 }^{ 0 }
=> { V }_{ 2 } = 3 m/s
83. The following figure shows the velocitytime plot for a particle travelling along a straight line. The distance covered by the particle from t = 0 s to t = 5 s is _______m.
(1 Mark, 2017[1])

Ans: 10
Explanation:
84. A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t^{2}; θ(t) = t, where t is time. The kinetic energy of the particle at t = 2 is
(a) 4
(b) 12
(c) 16
(d) 24
(1 Mark, 2017[1])

Ans: c
Explanation:
85. Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the centre of disk A to the velocity of the centre of disk B is
(a) \sqrt { \frac { 3 }{ 4 } }
(b) \sqrt { \frac { 3 }{ 2 } }
(c) 1
(d) \sqrt { 2 }
(2 Mark, 2017[1])

Ans: a
Explanation:
86. The rod PQ of length L = \sqrt { 2 }m, and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces OP and OQ. Assume acceleration due to gravity, g = 10 m/s^{2}. The mass moment of inertia of the rod about its centre of mass and an axis perpendicular to the plane of the figure is (ML^{2}/12). At this instant, the magnitude of angular acceleration (in radian/s^{2}) of the rod is ___.
(2 Mark, 2017[2])

Ans: 7.5
Explanation:
87. A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.
The tensions in the strings are
(a) T_{1} = 100 N and T_{2} = 0 N
(b) T_{1} = 0 N and T_{2} = 100 N
(c) T_{1} = 75 N and T_{2} = 25 N
(d) T_{1} = 25 N and T_{2} = 75 N
(1 Mark, 2018[1])
88. A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s^{2} and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of
(a) 1
(b) 2
(c) 4
(d) \infty
(2 Mark, 2018[1])

Ans: c
Explanation:
89. A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m) where the jet strikes the floor is
(a) 0.5
(b) 1.0
(c) 2.0
(d) 4.0
(2 Mark, 2018[1])

Ans: b
Explanation:
90. Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g = 10 m/s^{2}, the normal force (in N) at Q is _______ (correct to two decimal places).
(2 Mark, 2018[1])

Ans: 420
Explanation: