Consider the following statements A and B and identify the correct answer :(A) : In an elastic collision, if a body suffers a head on collision with another of same mass atrest, the first body comes to rest while the other starts moving with the velocity of the first one.(B) : Two bodies of equal mass suffering a head on elastic collision merely exchanges their velcities :

A. Both A and B are true

B. Both A and B are false

C. A is true but B is false

D. A is false but B is true

The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (2, 2, 2).The position of the fourth mass of 4 kg to be placed in the system as that the new centre of mass is at (0, 0, 0) is :

A. (-3,-3,-3)

B. (-3,3,-3)

C. (2,3,-3)

D. (2,-2,-3)

The machine gun fires 240 bullets per minute. If the mass of each bullet is 10 g and the velocity of the bullets is 600 ms-1, the power (in kW) of the gun is :

A. 43200

B. 432

C. 72

D. 7.2

A body of mass m is suspended to an ideal spring of force constant k. The expected change in the position of the body due to an additional force F acting vertically downwards is

A. 3F/2k

B. 2F/k

C. 5F/2k

D. 4F/k

The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficientof friction between the body and the inclined plane is 1/2√3 the angle of the inclined plane is :

A. 600

B. 450

C. 300

D. 150

A. ball of mass m moving with a velocity V*collides head on elastically with another of the same mass m but moving with a - V (in the opposite direction). After the collision :

A. the velocities are exchanged between the two balls

B. both the balls come to rest

C. both of them move at right angles to the original line of motion

D. one ball comes to rest and the other ball travels back with velocity 2V

A rifle of 20 kg mass can fire 4 bullets per second. The mass of each bullet is 35 x 10-3 kg and its final velocity is 400 ms-1. Then what force must be applied on the rifle so that it does not move backwards while firing the bullets

A. 80 N

B. 28 N

C. -112N

D. -56N

An object of mass 2 m is projected with a speed of 100 ms-1 at an angle θ = sin-1 (3/5) to the horizontal. At the highest point, the object breaks into two pieces of same mass m and the first one comes to rest. The distance between the point of projection and the point of landing of the bigger piece (in meter) is (Given g =10 m/s2)

A. 3840

B. 1280

C. 1440

D. 960

A 2 kg body and 3 kg body have equal momentum. If the kinetic energy of 3 kg body is 10 Joules, the kinetic energy of 2 kg body will be, (in joules) :

A. 6.66

B. 15

C. 22.5

D. 45

Two bodies of 6 kg and 4 kg masses have their velocity 5i^-2j^+10k^ and 10i^-2j^+5k^ respectively. Then the velocity of their centre of mass is

A. 5i ^+ 2j^ - 8k^

B. 7i^ + 2j^ - 8k^

C. 7i^ - 2j^+8k^

D. 5i^-2j^+8k^

In two separate collisions, the coefficient of restitutions e1 and e2 are in the ratio 3:1. In the first collision the relative velocity of approach is twice the relative velocity of separation, then the ratio between relative velocity of approach and the relative velocity of separation in the second collision is

A. 1 : 6

B. 2 : 3

C. 3 : 2

D. 6 : 1

A man slides down on a telegraphic pole with an acceleration equal to one-fourth of acceleration due to gravity. The frictional force between man and pole is equal to in terms of man's weight w

A. w/4

B. w/2

C. 3w/4

D. w

A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to 1/10th of its original velocity. Then the mass of the second body is

A. 4.09 kg

B. 0.5 kg

C. 5 kg

D. 5.09 kg

A particle of mass 4 m explodes into three pieces of masses m, m and 2 m. The equal masses move along X- and Y-axes with velocities 4 ms-1 and 6 ms-1 respectively. The magnitude of the velocity of the heavier mass is

A. √17 ms-1

B. 2√13 ms-1

C. √13 ms-1

D. √13 / 2 ms-1

A bullet of mass 0.02 kg travelling horizontally with velocity 250 ms_1 strikes a block of wood of mass 0.23 kg which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after traveling a distance of 40 m. The coefficient of sliding friction of the rough surface is

A. 0.75

B. 0.61

C. 0.51

D. 0.30

Center of mass of two particles with masses 2kg and 1kg located at (1,0,1) and (2,2,0) has the co-ordinates of

A. 4/3,2/3,2/3

B. 2/3,4/3,2/3

C. 2/3,2/3,4/3

D. 1/3,2/3,2/3

When the angle of inclination of an inclined plane is θ, an object slides down with uniform velocity. If the same object is pushed with a initial velocity u on the same inclined plane; it goes up the plane and stops at a certain distance on the plane. Thereafter the body :

A. slides down the inclined plane and reaches the ground with velocity u.

B. slides down the inclined plane and reaches the ground with velocity less than u.

C. slides down the inclined plane and reaches the ground with velocity greater than u.

D. stays at rest on the inclined plane and will not slide down.

A bullet of mass 10 g is fired horizontally with a velocity 1000ms-1 from a rifle situated at a height 50 m above the ground. If the bullet reaches the ground with a velocity 500ms-1, the work done against air resistance in the trajectory of the bullet is : (g=10ms-2)

A. 5005J

B. 3755J

C. 3750J

D. 17.5J

A solid wooden block resting on a frictionless surface is hit by a bullet. The bullet gets embedded. During this process:

A. only kinetic energy is conserved

B. only momentum is conserved

C. both momentum and kinetic energy are conserved

D. Neither momentum nor kinetic energy is conserved

An iron block of sides 50 cm x 8 cm x 15 cm has to be pushed along the floor. The force required will be minimum when the surface in contact with ground is:

A. 8 cm x 15 cm surface

B. 5 cm x 15 cm surface

C. 8 cm x 5 cm surface

D. force is same for all surface

A man 50 kg is standing at one end on a boat of length 25 m and mass 200 kg. If he starts running and when he reaches the other end, he has a velocity 2 ms-1 with respect to the boat.The final velocity of the boat is : (in ms-1)

A. 2/5

B. 2/3

C. 8/5

D. 8/3

The total mechanical energy of a harmonic oscillator of A=1m and force constant 200 N/m is 150J.Then

A. the minimum potential energy is zero

B. the minimum potential energy is 100J

C. the minimum potential energy is 50J

D. the miximum kinetic energy is 150J

A 1.0 HP IP motor pumps out water from a well of 30m and fills water tank of volume 2238 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is: (g= 10 ms-2)

A. 5 min

B. 10 min

C. 15 min

D. 20 min

The mass of a balloon with its contents is 15kg. It is descending with an acceleration equal to half that of acceleration due to gravity. If it is to go up with the same acceleration, keeping the volume same, its mass should be decreased by

A. 13 kg

B. l kg

C. 0.75 kg

D. 0.5 kg

A force of 5 N making an angle 8 with the horizontal acting on an object displaces it by 0.4 m along the horizontal direction. If the object gains kinetic energy of 1 J the horizontal component of the force is :

A. 1.5 N

B. 2.5 N

C. 3.5 N

D. 4.5 N

A uniform chain of length L is lying on the horizontal table. If the coefficient of friction between the chain and the table top is 'μ’ what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table

A. L / (1+μ )

B. μL / (1+μ)

C. L / (1 - μ)

D. μL / (1-μ)

A 2 kg stone tied at the end of a string of 1 m length, is whirled along a vertical circle at a constant speed of 4 m/s. The tension in the string has a value of 52 N when the stone is :

A. at the top of the circle

B. half way down

C. at the bottom of the circle

D. none of the above

A car of mass 400 kg and travelling at 72 kmph crashes into a truck of mass 4000 kg and travelling at 9 kmph, in the same direction. The car/bounces back at a speed of 18 kmph.The speed of truck after the impact is

A. 9 kmph

B. 18 kmph

C. 27 kmph

D. 36 kmph

A body of mass m1 moving with a velocity 10 ms-1 collides with another body at rest of mass m2 After collision the velocities of the two bodies are 2 ms-1 and 5 ms-1respectively, along the direction of motion of m1.The ratio m1/ m2

A. 5/12

B. 5/8

C. 8/5

D. 12/5

A mass of 12 kg at rest explodes into two pieces of masses 4 kg and 8 kg which move in opposite directions. If the velocity of 8 kg piece is 6 m/s, then the kinetic energy of the other piece is (in joule):

A. 64

B. 128

C. 144

D. 288