State if each of the following statements is true or false. Give reasons for your answer.

A. In an elastic collision of two bodies, the momentum and energy of each body is conserved.

B. Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

C. Work done in the motion of a body over a closed loop is zero for every force in nature.

D. In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

A ball of mass m, moving with a speed 2v₀, collides inelastically (e > 0) with an identical ball at rest. Show that

(a) For head-on collision, both the balls move forward.

(b) For a general collision, the angle between the two velocities of scattered balls is less than 90°.

During inelastic collision between two bodies, which of the following quantities always remain conserved?

Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed V as shown in Fig. 6.3.

If the collision is elastic, which of the following (Fig. 6.4) is a possible result after collision?

A small particle travelling with a velocity υ collides elastically with a spherical body of equal mass and of radius r initially kept at rest. The centre of this spherical body is located a distance ρ(< r) away from the direction of motion of the particle (figure
9-E23). Find the final velocities of the two particles.

[Hint: The force acts along the normal to the sphere through the contact. Treat the collision as one-dimensional for this direction. In the tangential direction no force acts and the velocities do not change].

A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head-on, the bodies go at right angle to each other after the collision.

Two blocks M₁ and M₂ having equal mass are free to move on a horizontal frictionless surface. M₂ is attached to a massless spring as shown in Fig. 6.10. Initially M₂ is at rest and M₁ is moving toward M₂ with speed v and collides head-on with M₂.

The bob A of a pendulum released from 30o to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.