Consider a two-particle system with particles having masses m1 and m2. If the first particle is pushed towards the centre of mass through a distance d, by what distance should the second particle be moved, so as to keep the centre of mass at the same position?

• 
• 

• d

• d

An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F_1/F₂ is

• R₁/R₂

• (R₁/R₂)²

• 1

• 1

A smooth block is released at rest on a 45° incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

The upper half of an inclined plane with inclination φ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

• 2sinφ

• 2cosφ

• 2tanφ
• 2tanφ

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

• 3.0 cm

• 2.0 cm

• 1.5 cm

• 1.5 cm

Out of the following pair, which one does NOT have identical dimensions is

• angular momentum and Planck’s constant

• impulse and momentum

• moment of inertia and moment of a force

• moment of inertia and moment of a force

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

• depends on height of breaking

• does not shift

• body C

• body C

A particle of mass 0.3 kg is subjected to a force F=−kx with k=15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

• 3 m/s²

• 15 m/s²

• 5 m/s²

• 5 m/s²

The block of mass M moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

• 

• KL²/2M

• zero

• zero

30.

A mass ‘m’ moves with a velocity v and collides inelastically with another identical mass. After collision, the 1^st mass moves with velocity v/√3 in a direction perpendicular to the initial direction of motion. Find the speed of the 2nd mass after collision

• v

• √3 v

• 2v/√3

• 2v/√3