Question

A body falling from a height of $10m$ rebounds from a hard floor. It loses $20$% of its energy in the impact. What could be the height to which it would rise after the impact?

• A. $7m$
• B. $5m$
• C. $8m$
• D. $6m$

Answer 1

The correct option is C $8m$

Initial potential energy $=mgh$ where $h=10m$

It loses $20$% of its energy$=0.2mgh$

Its kinetic energy after rebound$=0.8mgh=\frac{1}{2}m{v}^2$....(1)

Now the ball will rise to a new height 'h' and :

$\frac{1}{2}m{v}^2=mg{h}^{\prime }$.....(2)

From (1) and (2):

$0.8mgh=mg{h}^{\prime }$

$h^{\prime }=0.8h$

$=0.8\times 10=8m$