Question

A rubber ball is dropped from a height of $5m$ on a plane, where the acceleration due to gravity is not shown. On bouncing it rises to $1.8m$. The ball loses its velocity on bouncing by a factor of

• A. $\frac{16}{25}$
• B. $\frac{2}{5}$
  
• C. $\frac{3}{5}$
  
• D. $\frac{9}{25}$
  

Answer 1

The correct option is B $\frac{2}{5}$

Given

$h_1=5m$

$h_2=1.8$

Velocity of ball just before hitting the ground $=\sqrt{2g{h}_1}=\sqrt{10g}$

Velocity of ball just after hitting the ground $=\sqrt{2g{h}_2}=\sqrt{3.6g}$

Loss in velocity$=\frac{\sqrt{10g}-\sqrt{3.6g}}{\sqrt{10g}}=1-\frac{3}{5}=\frac{2}{5}$

Hence correct answer is option $B$