A ball dropped from a $20 m$ height loses $40$ % of its energy on hitting the ground. Upto what height does the ball rebound?

28 m

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8 m

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12 m

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20 m

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Solution

The correct option is C $12 m$
Initial $P E = m g = 20 m g$
It loses $40$ % of its energy $= 0.4 \times 20 m g = 8 m g$
Remaining energy is used as KE as rebound:
$12 m g = \frac{1}{2} m v^{2}$
The ball now reaches a height 'h':
$\frac{1}{2} m v^{2} = m g h^{'} = 12 m g$
$h^{'} = 12 m$

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A ball dropped from a 20m height loses 40% of its energy on hitting the ground. Upto what height does the ball rebound?

The correct option is C 12mInitial PE=mg=20mgIt loses 40% of its energy=0.4×20mg=8mgRemaining energy is used as KE as rebound:12mg=12mv2The ball now reaches a height 'h':12mv2=mgh′=12mgh′=12m

A ball dropped from a $20 m$ height loses $40$ % of its energy on hitting the ground. Upto what height does the ball rebound?

The correct option is C $12 m$
Initial $P E = m g = 20 m g$
It loses $40$ % of its energy $= 0.4 \times 20 m g = 8 m g$
Remaining energy is used as KE as rebound:
$12 m g = \frac{1}{2} m v^{2}$
The ball now reaches a height 'h':
$\frac{1}{2} m v^{2} = m g h^{'} = 12 m g$
$h^{'} = 12 m$