1. A car starting from rest is accelerated at a constant rate α until it attains a speed v. It is then retarded at a constant rate β until it comes to rest. Then the average speed of the car during its entire journey is
1) 0 2) αv/2β 3) βv/2α 4) v/2
2. A body is dropped from the roof of a multi storeyed building. It passes the ceiling of the 15th storey at a speed of 20 ms-1. If the height of each storey is 4 m, the number of storeys in the building is (take g = 10 ms-2 and neglect air resistance)
1) 20 2) 25 3) 30 4) 35
3. The co-ordinates of a moving particle at any time t are x = αt3 and y = βt3 where α and β are constants. Then the speed of the particle at time t is 
4. A truck carrying sand is moving on a smooth horizontal road with a uniform speed u. If a mass ∆m of sand leaks in a time ∆t from the bottom of the truck, the force needed to keep the truck moving at a uniform speed u is given by 
5. A string passing over a light frictionless pulley carries two masses m1 = 5 kg and m2 = 4.8 kg at its ends hanging vertically. When the masses are released, their acceleration will be (in ms-2)
1) 0.2 2) 9.8 3) 5 4) 4.8
6. A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 ms-1 with respect to the man. The speed of the man with respect to the surface is
1) 0.10 ms-1 2) 0.20 ms-1 3) 0.40 ms-1 4) 0.14 ms-1
7. A particle starts from origion O from rest and moves with a uniform acceleration along the positive X - axis. Which of the following curve/curves represents its motion?
1) i, ii , iii 2) ii, iii, iv 3) i, ii, iv 4) i, ii, iii, iv
8. Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively from a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum area covered by the bullets fired by the two guns on the ground is
1) 1 : 2 2) 1 : 4 3) 1 : 16 4) 16 : 1
9. Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum weights h1 and h2. Which of the following is correct?
1) R2 = h1h2 2) R2 = 2 h1h2 3) R2 = 4 h1h2 4) R2 = 16 h1h2
10. A pendulum consists of a wooden bob of mass m and of length l. A bullet of mass m1 is fired towards the pendulum with a speed v1. The bullet emerges out of the The bullet emerges out of the bob with a speed v1/3 and the bob just com pletes motion along a vertical circle. Then v1 is 
11. A spring of force constant ‘K’ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of
1) (2/3)K 2) (3/2)K 3) 3K 4) 4K
12. A force exerts an impulse I on a particle changing its speed from u to 2u. The applied force and the initial velocity are oppositely directed along the same line. Then the work done by the force is
1) 0 2) Iu 3) 2 Iu 4) 1/2 Iu
13. The figure shows a uniform rod lying along the X - axis. The locus of all the points lying on the XY - plane, about which the moment of inertia of the rod is same as that about O is
1) A circle 2) A parabola 3) An ellipse 4) A straight line
14. A uniform rod of mass m and length l hinged at its end is released from rest when it is in the horizontal position. The normal reaction at the hinge when the rod becomes vertical is
1) mg 2) mg/2 3) 3mg/2 4) 5mg/2
15. A carpet of mass M, made of an inextensible material is rolled along its length in the form of a cylinder of radius R and kept on a rough floor. If the carpet is unrolled, with out sliding, to a radius R/2, the decrease in potential energy is
1) 1/2 MgR 2) 5/8 MgR 3) 3/4 MgR 4) 7/8 MgR
16. A solid cylinder of mass M and radius R rolls down an inclined plane of height h. The angular velocity of the cylinder when it reaches the bottom of the plane will be 
17. A uniform rod of length L is suspended from one end such that it is free to rotate about an axis passing through that end and perpendicular to the length. What minimum speed must be imparted to the lower and so that the rod completes one full rev
olution?
18. If the gravitational force of attraction between any two bodies were to vary as 1/r3 instead of 1/r2, the period of revolution of a planet round the sun would vary as
1) r1/2 2) r 3) r3/2 4) r2
19. A body is resting on a top of a hemispherical mound of ice of radius R. If ice is frictionless, what minimum horizontal velocity must be imparted to the body so that it leaves the mound without sliding over it? 
20. Find the height of the point vertically above the earth’s surface at which the acceleration due to gravity becomes 1% of its value at the surface? (Let R be the radius of the earth)
1) 8R 2) 9R 3) 10R 4) 99R
21. A solid sphere and solid cylinder of indentical radii approach an incline with the same linear velocity. Both roll without slipping all throughout. The two climb maximum heights h1 and h2 on the incline. Then h1/h2 is 
1) 4/5 2) 2/√5 3) 1 4) 14/15
22. A 70 kg person standing on ice throws a 3 kg body horizontally at 8 m/s. The coefficient of friction between the ice and his feat is 0.02. The distance the man slips is
1) 0.1 m 2) 1 m 3) 0.3 m 4) 0.4 m
23. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. Then, the time period of the second satellite is larger than that of the first one by (approximately)
1) 0.5% 2) 1% 3) 1.5% 4) 3%
24. A particle starts sliding down a frictionless inclined plane. If Sn is the distance travelled by it from time t = n - 1 sec to t = n 
25. A policeman moving on a road with a speed of 30 kmph fires a bullet at a theif car speeding away in the same direction with a speed of 192 kmph. If the speed of the bullet is 150 ms-1, with what speed does the bullet hit the theif’s car?
1) 90 ms-1 2) 105 ms-1 3) 120 ms-1 4) 125 ms-1
26. A ball rolls off the top of a stair case with a horizontal velocity u m/s. If the steps are h metre high and b metre wide the ball will hit the edge of the nth step, if ...... 
27. A golfer standing on a level ground hits a ball with a velocity of u = 52 m/s at an angle α above the horizontal. If tan α = 5/12, then the time for which the ball is at least 15 m above the ground will be ........... (take g = 10 m/s2)
1) 1s 2) 2s 3) 3s 4) 4s
28. A particle is projected with a certain velocity at an angle α above the horizontal from the foot of an inclined plane of inclination 30°. If the particle strikes the plane normally, then α is
1) 45° 2) 60° 3) 30° + tan-1(√3/2) 4) 30° + tan-1 (2√3)
29. Two masses each equal to m are lying on X - axis at (-a, 0) and (+a, 0) respectively as shown in the figure. They are connected by a light string. A force F is applied at the origin along the vertical direction. As a result, the masses move towards each other without loosing contact with ground. Then the acceleration of each mass is (assume the instantaneous position of the masses as (-x, 0) and (x, 0) respectively)
30. A body A with a momentum P collides with another identical stationary body B one dimensionally. During the collision, B gives an impulse J to the body A. Then the coefficient of restitution is
1) J/P + 1 2) 2) 2J/P -1 3) J/P - 1 4) J/2P - 1
31. A uniform rod of mass m, length l rests on a smooth horizontal surface. Rod is given a sharp horizontal impulse p perpendicular to the rod at a distance l/4 from the centre. The angular velocity off the rod will be
1) p/ml 2) p/2ml 3) 2p/ml 4) 3p/ml
ANSWERS: 1-4; 2-1; 3-4; 4-4; 5-1; 6-2; 7-3; 8-3; 9-4; 10-3; 11-2; 12-4; 13-1; 14-4; 15-4; 16-3; 17-3; 18-4; 19-2; 20-2; 21-4; 22-3; 23-3; 24-1; 25-2; 26-2; 27-2; 28-3; 29-3; 30-2; 31-4.
