A ball of density d is dropped on to a horizontal solid surface. It bounces elastically from the surface and returns to its original position in a time `t_1`. Next, the ball is released and it falls through the same height before striking the surface of a liquid of density of `d_L`
(a) If `dltd_L`, obtain an expression (in terms of d, `t_1` and `d_L`) for the time `t_2` the ball takes to come back to the position from which it was released.
(b) Is the motion of the ball simple harmonic?
(c) If `d=d_L`, how does the speed of the ball depend on its depth inside the liquid? Neglect all frictional and other dissipative forces. Assume the depth of the liquid to be large.

Options

A. Does not vary with depth.
B. Increases with depth.
C. Decreases with depth.
D. All of the above options are incorrect

Answer

A

Explanation

When ` d_L = d `, retardation or acceleration inside the liquid becomes zero (upthrust = weight).
Therefore, the ball will continue to move with constant velocity ` v = g t _ 1 //2 ` inside the liquid.