Question

A handball falls on the ground and rebounds elastically along the same line of motion. Then? (This question has multiple correct options).
A. The linear momentum of the universe remains conserved.
B. The linear momentum of the ball is not conserved.
C. During the collision, the whole kinetic energy of the ball is converted into potential energy and then completely converted into kinetic energy of the ball.
D. During the collision, the kinetic energy remains constant.

Answer 1

Hint:Recall the concept of elastic collision of two objects and law of conservation of linear momentum. Using these concepts, check the information about the conservation of linear momentum of the system of the two objects in collision, conservation of kinetic energy of the system of the objects in collision and individual energy of the system of the two objects in collision.

Complete answer:
When a handball collides with the ground elastically, it exerts a force on the ground. When the handball rebounds from the ground, the ground exerts an equal and opposite force on the handball. This makes the net force acting on the handball-ground system zero.Therefore, the linear momentum of the universe remains conserved.Hence, the statement given in the option A is correct.

If the handball hits the ground with a velocity v then the handball rebounds from the ground with the same velocity v in the opposite direction. Hence, the magnitude of the change in linear momentum of the handball is 2mv. This change in momentum of the ball occurs due to the force exerted by the ball on the ground. For the linear momentum of the handball to be conserved, the change in linear momentum of the ball should be zero.Therefore, the linear momentum of the handball is not conserved.Hence, the statement given in the option B is correct.

When the ball hits the ground, it rebounds from the ground with some velocity v. Hence. The ball has kinetic energy when it is at the ground. But the potential energy of the ball becomes zero at this point. When the ball rebounds from the ground and reaches the maximum height. At this maximum height, the velocity of the ball is zero and the ball has only potential energy. Here, the kinetic energy of the ball at the ground is completely converted into potential energy according to the law of conservation of energy.When the ball again hits the ground, its potential energy converts into kinetic energy again to conserve the energy of the ball-ground system.Hence, the statement given in option C is correct.

The collision between the ball and the ground is elastic. In the elastic collision, the total kinetic energy of the ball-ground system is conserved but the kinetic energy of the individual ball or the ground is not conserved.Hence, the statement given in the option D is incorrect.

Hence, the options A, B and C are correct.

Note:The students should keep in mind that the linear momentum of the individual object in the elastic collision is not conserved. The linear momentum of the system is conserved. The same thing is applicable for kinetic energy. The kinetic energy of the individual object in the system is not conserved but the kinetic energy of the system is conserved.