Question

A ball hits the floor and rebounds after an inelastic collision. In this case,

• A. The momentum of the ball just after the collision is same as that just before the collision.
• B. The kinetic energy of the ball remains the same during the collision.
• C. The total momentum of the ball and the earth is conserved.
• D. None of the above

Answer 1

The correct option is C The total momentum of the ball and the earth is conserved.


As we know, for an inelastic collision, $0<e<1$
$e=\frac{\text{relative speed of seperation}}{\text{relative speed of approach}}=\frac{0-v}{u-0}$
Here $u$ is the speed just before the collision.
$v$ is the speed just after the collision.
$v=-ue$

a) Momentum before the collision $=\left(mu\right)$
Momentum just after the collision $=mv=(-mue)$
Hence, momentum of the ball will not be the same before and after the collision.

b) Kinetic energy just before the collision $=\frac{1}{2}m{u}^2$
Kinetic energy just after the collision $=\frac{1}{2}m{v}^2=\frac{1}{2}m(eu{)}^2$
Hence, kinetic energies will be different just before and after the collision.

c) As we know, if there is no external force is present, then momentum of the system will be conserved.
Here (ball + earth) is the system.

Hence, option (c) is correct.