1. Match the correct pairs between List I and List II.
(a) A – 4, B – 2, C – 3, D – 5
(b) A – 3, B – 1, C – 5, D – 2
(c) A – 5, B – 1, C – 2, D – 4
(d) A – 1, B – 2, C – 5, D – 4
(1 Mark, 1990)

Ans: a
2. Figure below shows a rigid bar hinged at A and supported in a horizontal by two vertical identical steel wires. Neglect the weight of the beam. The tension T_{1} and T_{2} induced in these wires by a vertical load P applied as shown are
(a) T_{1} = T_{2} = \frac { P }{ 2 }
(b) T_{1} = \frac { Pal }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right) } , T_{2} = \frac { Pbl }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right) }
(c) T_{1} = \frac { Pbl }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right) } , T_{2} = \frac { Pal }{ \left( { a }^{ 2 }+{ b }^{ 2 } \right) }
(d) T_{1} = \frac { Pal }{ 2\left( { a }^{ 2 }+{ b }^{ 2 } \right) }, T_{2} = \frac { Pal }{ 2\left( { a }^{ 2 }+{ b }^{ 2 } \right) }
(2 Mark, 1994)

Ans: b
Explanation:
3. A spring scale indicates a tension T in the right hand cable of the pulley system shown in figure below. Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass m is:
(a) 2T/g
(b) T(1 + c^{4π})/g
(c) 4T/g
(d) none of these
(2 Mark, 1995)

Ans: c
Explanation:
4. A ball of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact
(a) The velocity of ball A is \frac { 1 }{ 2 } \sqrt { 2gh }
(b) The velocity of ball A is zero
(c) The velocity of both balls is \frac { 1 }{ 2 } \sqrt { 2gh }
(d) None of the above
(1 Mark, 1996)

Ans: c
Explanation:
5. AB and CD are two uniform and identical bars of mass 10 kg each, as shown in Figure. The hinges at A and B are frictionless. The assembly is released from rest and motion occurs in the vertical plane. At the instant that the hinge B passes the point B, the angle between the two bars will be
(a) 60 degrees
(b) 37.4 degrees
(c) 30 degrees
(d) 45 degrees
(2 Mark, 1996)

Ans: a
As the hinge ‘B’ is frictionless, so no torque is applied to bar CD, so no angle change occurs.
The angle is 90 – 30 = 60
6. A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque T. If the coefficient of kinetic friction is μ, the friction force from the ground on the wheel is:
(a) μmg
(b) T/r
(c) zero
(d) None of these
(1 Mark, 1996)

Ans: a
Explanation:
7. A mass of 35 kg is suspended from a weightless bar AC, which is supported by a cable CB and a pin at A as shown in the Figure. The pin reactions at A on the bar AC are
(a) R_{x} = 343.4 N, R_{y} = 755.4 N
(b) R_{x} = 343.4 N, R_{y} = 0
(c) R_{x} = 755.4 N, R_{y} = 343.4 N
(d) R_{x} = 755.4 N, R_{y} = 0
(2 Mark, 1997)

Ans: d
8. A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. The acceleration of the car is:
(a) 7 m/s^{2}
(b) 50 m/s^{2}
(c) 25 m/s^{2}
(d) 10 m/s^{2}
(1 Mark, 1998)

Ans: d
Explanation:
9. A shown in Figure, a person A is standing at the centre of a rotating platform facing person B who is riding a bicycle, heading East. The relevant speeds and distances are shown in the given figure. At the instant under consideration, what is the apparent velocity of B as seen by A?
(a) 3 m/s heading East
(b) 3 m/s heading West
(c) 8 m/s heading East
(d) 13 m/s heading East
(2 Mark, 1999)

Ans: d
Explanation:
10. A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in Newton, necessary to roll the wheel along the rail is
(a) 0.5
(b) 5
(c) 15
(d) 150
(1 Mark, 2000)

Ans: d
Explanation:
11. The ratio of tension on the tight side to that on the slack side in a flat belt drive is:
(a) Proportional to the product of coefficient of friction and lap angle
(b) An exponential function of the product of coefficient of friction and lap.angle
(c) Proportional to the lap angle
(d) Proportional to the coefficient of friction
(1 Mark, 2000)

Ans: b
Explanation:
12. A truss consists of horizontal members (AC, CD, DB and EF) and vertical members (CE and DF) having length l each. The members AE, DE and BF are inclined at 45° to the horizontal. For the uniformly distributed load ‘p’ per unit length on the member EF of the truss shown in figure given below, the force in the member CD is
(a) pl/2
(b) pl
(c) 0
(d) 2pl/3
(1 Mark, 2003)

Ans: a
Explanation:
Data for Q.13 – 14 are given below.
A reel of mass ‘m’ and radius of gyration ‘k’ is rolling down smoothly from rest with one end of the thread wound on it held in the ceiling as depicted in the figure. Consider the thickness of the thread and its mass negligible in comparison with radius ‘r’ of the hub and the reel mass ‘m’. Symbol ‘g’ represents the acceleration due to gravity.
13. The linear acceleration of the reel is
(a)\frac { g{ r }^{ 2 } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(b)\frac { g{ k }^{ 2 } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(c)\frac { g{ rk } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(d)\frac { mg{ { r }^{ 2 } } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(1 Mark, 2003)

Ans: a
14. The tension in the thread is
(a) \frac { mg{ { r }^{ 2 } } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(b) \frac { mg{ rk } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(c) \frac { mg{ k }^{ 2 } }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(d) \frac { mg }{ ({ r }^{ 2 }+{ k }^{ 2 }) }
(1 Mark, 2003)

Ans: c
Explanation:
15. A bullet of mass ‘m’ travels at a very high velocity v (as shown in the figure) and gets embedded inside the block of mass ‘M’ initially at rest on a rough horizontal floor. The block with the bullet is seen to move a distance ‘s’ along the floor. Assuming μ to be the coefficient to kinetic friction between the block and the floor and ‘g’ the acceleration due to gravity. What is the velocity v of the bullet?
(a) \frac { M+m }{ m } \sqrt { 2\mu gs }
(b) \frac { Mm }{ m } \sqrt { 2\mu gs }
(c) \frac { \mu (M+m) }{ m } \sqrt { 2\mu gs }
(d) \frac { M }{ m } \sqrt { 2\mu gs }
(1 Mark, 2003)

Ans: a
Explanation:
16. The time variation of the position of a particle in rectilinear motion is given by x = 2t^{3} + t^{2} + 2t. If v is the velocity and a the acceleration of the particle in consistent units, the motion started with
(a) v = 0, a = 0
(b) v = 0, a = 2
(c) v = 2, a = 0
(d) v = 2, a = 2
(1 Mark, 2005)

Ans: d
Explanation:
17. The figure shows a pinjointed plane truss loaded at the point M by hanging a mass of 100 kg. The member LN of the truss is subjected to a load of
(a) 0 Newton
(b) 490 Newtons in compression
(c) 981 Newtons in compression
(d) 981 Newtons in tension
(1 Mark, 2004)

Ans: a
Explanation:
18. An ejector mechanism consists of a helical compression spring having a spring constant of K = 981 × 10^{3} N/m. It is precompressed by 100 mm from its free state. If it is used to eject a mass of 100 kg held on it, the mass will move up through a distance of
(a) 100 mm
(b) 5000 mm
(c) 981 mm
(d) 1000 mm
(2 Mark, 2004)

Ans: b
Explanation:
19. A rigid body shown in the Fig.(a) has a mass of 10 kg. It rotates with a uniform angular velocity ‘w ’. A balancing mass of 20 kg is attached as shown in Fig. (b). The percentage increase in mass moment of inertia as a result of this addition is
(a) 25%
(b) 50%
(c) 100%
(d) 200%
(2 Mark, 2004)

Ans: b
Explanation:
20. The figure shows a pair of pin jointed gripper tongs holding an object weighing 2000 N. The coefficient of friction (μ) at the gripping surface is 0.1. XX is the line of action of the input force and YY is the line of application of gripping force. If the pin joint is assumed to be frictionless, the magnitude of force F required to hold the weight is
(a) 1000 N
(b) 2000 N
(c) 2500 N
(d) 5000 N
(2 Mark, 2004)

Ans: d
Explanation:
21. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is
(a) Zero
(b) 2.5 N
(c) 5 N
(d) 25 N
(1 Mark, 2005)

Ans: c
Explanation:
22. Two books of mass 1 kg each are kept on a table, one over the other. The coefficient of friction on every pair of contacting surfaces is 0.3. The lower book is pulled with a horizontal force F. the minimum value of F for which slip occurs between the two books is
(a) Zero
(b) 1.06 N
(c) 5.74 N
(d) 8.83 N
(2 Mark, 2005)

Ans: d
Explanation:
23. A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3m/s, while the barrel is swinging upwards with a constant angular velocity of 2 rad/sec. The magnitude of the absolute velocity of the shell is
(a) 3 m/s
(b) 4 m/s
(c) 5 m/s
(d) 7 m/s
(2 Mark, 2005)

Ans: c
Explanation:
24. An elevator (lift) consists of the elevator cage and a counter weight, of mass m each. The cage and the counterweight are connected by a chain that passes over a pulley. The pulley is coupled to a motor. It is desired that the elevator should have a maximum stopping time of t seconds from a peak speed v. if the inertia of the pulley and the chain are neglected, the minimum power that the motor must have is
(a) \frac { 1 }{ 2 } m{ v }^{ 2 }
(b) \frac { m{ v }^{ 2 } }{ 2t }
(c) \frac { m{ v }^{ 2 } }{ t }
(d) \frac { 2m{ v }^{ 2 } }{ t }
(2 Mark, 2005)

Ans: c
Explanation:
25. A 1 kg mass of clay, moving with a velocity of 10 m/s, strikes a stationary wheel and sticks to it. The solid wheel has a mass of 20 kg and a radius of 1 m. Assuming that the wheel and the ground are both rigid and that the wheel is set into pure rolling motion, the angular velocity of the wheel immediately after the impact is approximately
(a) Zero
(b) 1/3 rad/s
(c) \sqrt { \frac { 10 }{ 3 }}rad/s
(d) \frac { 10 }{ 3 }rad/s
(2 Mark, 2005)

Ans: b
Explanation:
26. If a system is in equilibrium and the position of the system depends upon many independent variables, the principle of virtual work states that the partial derivatives of its total potential energy with respect to each of the independent variable must be
(a) 1.0
(b) 0
(c) 1.0
(d)\infty
(2 Mark, 2006)

Ans: b
Explanation:
27. If point A is in equilibrium under the action of the applied forces, the values of tensions T_{AB} and T_{AC} are respectively.
(a) 520 N and 300 N
(b) 300 N and 520 N
(c) 450 N and 150 N
(d) 150 N and 450 N
(2 Mark, 2006)

Ans: a
Explanation:
28. During inelastic collision of two particles, which one of the following is conserved?
(a) Total linear momentum only
(b) Total kinetic energy only
(c) Both linear momentum and kinetic energy
(d) Neither linear momentum nor kinetic energy
(1 Mark, 2007)

Ans: a
Explanation:
29. A block of mass M is released from point P on a rough inclined plane with inclination angle θ, shown in the figure below. The coefficient of friction is μ. If μ < tanθ, then the time taken by the block to reach another point Q on the inclined plane, where PQ = s, is
(a) \sqrt { \frac { 2s }{ gcos\theta (tan\theta \mu ) } }
(b) \sqrt { \frac { 2s }{ gcos\theta (tan\theta +\mu ) } }
(c) \sqrt { \frac { 2s }{ gsin\theta (tan\theta \mu ) } }
(d) \sqrt { \frac { 2s }{ gsin\theta (tan\theta +\mu ) } }
(2 Mark, 2007)

Ans: a
Explanation:
30. A straight rod of length L(t), hinged at one end and freely extensible at the other end, rotates through an angle θ(t) about the hinge. At time t, L(t) =1m, \dot { L }(t) = 1m/s, θ(t) = π/4 rad and \dot { \theta }(t) = 1 rad/s. The magnitude of the velocity at the other end of the rod is
(a) 1 m/s
(b) \sqrt { 2 } m/s
(c) \sqrt { 3 } m/s
(d) 2 m/s
(1 Mark, 2008)

Ans: b
Explanation: