Question

A small ball rolls off the top landing of the staircase. If strikes the mid- point of the first step and then the mid - point of the second step. The steps are smooth, and identical in height and width. The coefficient of restitution between the ball and the first step is

• A. 1
• B. $\frac{3}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{3}{4}$


C to D $v_2=\sqrt{2gx}=gt\therefore t=\frac{v_2}{g}$
From A to B, time will become two times.
Applying $S=ut+\frac{1}{2}a{t}^2$ in vertical direction, we have
$-x=\left(e{v}_2\right)\left(2t\right)-\frac{1}{2}\times g\times (2t{)}^2$
$-x=\frac{2e{v}_2^2}{g}-\frac{2v_2^2}{g}$
$-x=2e\left(2x\right)-2\left(2x\right)$
$\therefore e=\frac{3}{4}$