Question

A ball strikes a smooth horizontal floor obliquely and rebounds inelastically, then choose the correct statement(s)

• A. The kinetic energy of the ball just after hitting the floor is equal to the potential energy of the ball at its maximum height after rebound.
• B. Total energy of the ball is not conserved.
• C. The angle of rebound with the vertical is greater than the angle of incidence.
• D. None of the above.

Answer 1

Answer: (B), (C)

The angle of rebound with the vertical is greater than the angle of incidence.

Let $\alpha$ be the angle with which ball strikes the floor with the vertical,
velocity at the instant of striking the floor be $u$ and
Rebound velocity be $v$ at angle $\beta$ with the vertical as shown.

Since the floor is smooth, therefore horizontal componet of velocity remains unchanged.
Hence
$v\sin \beta =u\sin \alpha ...\left(i\right)$
Since, the floor is inelastic, therefore normal component of velocity just after the collision is less than that just before the collision. Hence,
$v\cos \beta <u\cos \alpha ...\left(ii\right)$
Dividing Eq. $\left(i\right)$ by Eq. $\left(ii\right),$
$\tan \beta >\tan \alpha$
$\beta >\alpha$
Hence, option (c) is correct.
Since the ball has a horizontal component of velocity, therefore, at highest point, its kinetic energy is not equal to zero.
It means, at highest point, potential energy of the ball is less than the kinetic energy just after rebound. Hence, option (a) is incorrect.
Since the collision is inelastic, there is some loss of energy during the collision.
Hence, the total energy of the ball does not remain conserved.
So, option (b) is also correct.