Question

From a height of $5m$ a ball is thrown vertically downwards with an initial velocity of $10m/s$ towards a hard horizontal floor. If it bounces to the same height, then the coefficient of restitution is $(g=10m{s}^{-2})$

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

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$


$e=\frac{v_2-v_1}{u_1-u_2}$

Here, the $u_1$ and $u_2$ are the velocities of ball and floor before collision, while $v_1$ and $v_2$ are the velocitites of ball and floor after collision.

$u_2=0,v_2=0,u_1=?,v_1=?$

$u_1^2=u^2+2gh$

$u_1=-\sqrt{100+2\times 10\times 5}=-10\sqrt{2}m/s$

After collision, ball will just cover height $h=5m$, so we can write:
$0-v_1^2=2gh$

$v_1=\sqrt{2gh}=\sqrt{2\times 10\times 5}=10m/s$

$\therefore e=\frac{0-10}{-10\sqrt{2}-0}=\frac{1}{\sqrt{2}}$