31. A circular disk of radius R rolls without slipping at a velocity V. The magnitude of the velocity at point P (see figure) is:
(a) \sqrt { 3 } V
(b) \frac { \sqrt { 3 } V }{ 2 }
(c) \frac { V }{ 2 }
(d) \frac { 2V }{ \sqrt { 3 } }
(2 Mark, 2008)

Ans: a
Explanation:
33. A block weighing 981N is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is μ = 0.2. A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100N. What will be the tension, T (in N) in the cable if the man is just able to move the block to the right?
(a) 176.2
(b) 196.0
(c) 481.0
(d) 981.0
(1 Mark, 2009)

Ans: c
Explanation:
34. A uniform rigid rod of mass M and length L is hinged at one end as shown in the adjacent figure. A force P is applied at a distance of 2L/3 from the hinge so that the rod swings to the right. The reaction at the hinge is
(a) –P
(b) 0
(c) P/3
(d) 2P/3
(2 Mark, 2009)

Ans: b
Explanation:
35. The coefficient of restitution of a perfectly plastic impact is
(a) 0
(b) 1
(c) 2
(d) \infty
(1 Mark, 2011)

Ans: a
Explanation:
36. A stone with mass of 0.1kg is catapulted as shown in the figure. The total force F_{x} (in N) exerted by the rubber band as a function of distance x (in m) is given by F_{x} = 300x^{2}. If the stone is displaced by 0.1m from the unstretched position (x=0) of the rubber band, the energy stored in the rubber band is
(a) 0.01J
(b) 0.1J
(c) 1J
(d) 10J
(2 Mark, 2011)

Ans: b
Explanation:
37. A 1 kg block is resting on a surface with coefficient of friction μ = 0.1. A force of 0.8N is applied to the block as shown in figure. The friction force is
(a) 0
(b) 0.8N
(c) 0.98N
(d) 1.2N
(2 Mark, 2011)

Ans: b
Explanation:
38. A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is
(a) Zero
(b) rα
(c) \sqrt { { (r\alpha ) }^{ 2 }+{ (r{ \omega }^{ 2 }) }^{ 2 } }
(d) r{ \omega }^{ 2 }
(1 Mark, 2012)

Ans: d
Explanation:
39. A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is
(a) 395
(b) 790
(c) 1580
(d) 3160
(1 Mark, 2012)

Ans: b
Explanation:
Common Data for Questions 40 and 41:
Two steel truss members, AC and BC, each having cross sectional area of 100 mm^{2}, are subjected to a horizontal force F as shown in figure. All the joints are hinged.
40. If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is
(a) 0.63
(b) 0.32
(c) 1.26
(d) 1.46
(2 Mark, 2012)

Ans: a
Explanation:
41. The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is
(a) 8.17
(b) 11.15
(c) 14.14
(d) 22.30
(2 Mark, 2012)

Ans: b
Explanation:
42. A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10^{4} seconds. The amplitude in mm of the resulting free vibration is
(a) 0.5
(b) 1.0
(c) 5.0
(d) 10.0
(2 Mark, 2013)

Ans: c
Explanation:
43. A pin jointed uniform rigid rod of weight W and length is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is
(a) zero
(b) W/4
(c) W/2
(d) W
(2 Mark, 2013)

Ans: b
44. A circular object of radius ‘r’ rolls without slipping on a horizontal level floor with the centre having velocity V. The velocity at the point of contact between the object and the floor is
(a) Zero
(b) V in the direction of motion
(c) V opposite to the direction of motion
(d) V vertically upward from the floor
(1 Mark, 2014[1])

Ans: a
Explanation:
45. A block R of mass 100 kg is placed on a block S of mass 150kg as shown in the figure. Block R is tied to the wall by a mass less and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4 the minimum force F (in KN) needed to move the block S is
(a) 0.69
(b) 0.88
(c) 0.98
(d) 1.37
(2 Mark, 2014[1])

Ans: d
Explanation:
46. A block weighing 200 N is in contact with a level plane whose coefficients of static and kinetic friction are 0.4 and 0.2, respectively. The block is acted upon by a horizontal force (in Newton) P = 10t, where t denotes the time in seconds. The velocity (in m/s) of the block attained after 10 seconds is_____.
(2 Mark, 2014[1])

Ans: 4.905
Explanation:
47. A two member truss ABC is shown in the figure. The force (in kN) transmitted in member AB is _____.
(1 Mark, 2014[2])

Ans: 20
Explanation:
48. A truck accelerates up a 10° incline with a crate of 100 kg. Value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration (in m/s^{2}) of the truck such that the crate does not slide down is _____.
(2 Mark, 2014[2])

Ans: 1.19
Explanation:
49. A rigid link PQ of length 2 m rotates about the pinned end Q with a constant angular acceleration of 12 rad/s^{2}. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s^{2}) of the end P is __.
(2 Mark, 2014[2])

Ans: 40
Explanation:
50. A mass m_{1} of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m_{2} of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is
(a) 0.6
(b) 0.1
(c) 0.01
(d) 0
(1 Mark, 2014[3])

Ans: d
Explanation:
51. An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is
(a) \frac { 9 }{ 16 }mv^{2}
(b) \frac { 11 }{ 16 } mv^{2}
(c) \frac { 13 }{ 16 } mv^{2}
(d) \frac { 15 }{ 16 } mv^{2}
(2 Mark, 2014[3])

Ans: c
Explanation:
52. A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane is ____.
(2 Mark, 2014[3])

Ans: 57.8
Explanation:
53. For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The force (in kN) in the member QS is (All dimensions are in m)
(a) 11.25 tension
(b) 11.25 compression
(c) 13.5 tension
(d) 13.5 compression
(2 Mark, 2014[4])

Ans: a
Explanation:
54. A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis 1m from its end as shown in the figure. The magnitude of the angular acceleration (in rad/s^{2}) of the rod at the position shown is _______.
(2 Mark, 2014[4])

Ans: 2.05
Explanation:
55. A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the YY axis, stands on a rough level floor as shown in the figure. A force P is applied at midheight on the wardrobe so as to tip it about point Q without slipping. What are the minimum values of the force (in newton) and the static coefficient of friction μ between the floor and the wardrobe, respectively?
(a) 490.5 and 0.5
(b) 981 and 0.5
(c) 1000.5 and 0.15
(d) 1000.5 and 0.25
(2 Mark, 2014[4])

Ans: a
56. A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B) and the wall (A), the magnitude of the force P (in newton) required to maintain equilibrium of the ladder is _____.
(2 Mark, 2014[4])

Ans: 400
Explanation:
57. A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is ______.
(1 Mark, 2015[1])

Ans: 20
Explanation:
58. Two identical trusses support a load of 100 N as shown in the figure. The length of each truss is1.0 m; crosssectional area is 200 mm^{2}; Young’s modulus E = 200 GPa. The force in the truss AB (in N) is _________
(1 Mark, 2015[1])

Ans: 100
Explanation:
59. A swimmer can swim 10 km in 2 hours when swimming along the flow of a river. While swimming against the flow, she takes 5 hours for the same distance. Her speed in still water (in km/h) is _____.
(1 Mark, 2015[1])

Ans: 3.5
Explanation:
60. A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is
(2 Mark, 2015[1])

Ans: 0.64
Explanation: