A bolt of mass $0.2 k g$ falls from the ceiling of an elevator moving down with an uniform speed of $5 m s^{- 1}$ . It hits the floor of the elevator (length of the elevator $= 5 m)$ and does not rebound. The amount of heat produced by the impact is (Take $g = 10 m s^{- 2})$ .

5 J

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10 J

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15 J

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20 J

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Solution

The correct option is D $20 J$
Given data,
$m a s s = 0.2 k g$
Uniform speed $= 5 m / s$
It hits the floor of the elevator (length of the elevator $= 5 m$ )
$g = 10 m / s^{2}$
$h = 5 m$
Since, the relative velocity of the both with respect to the lift is zero. at the time of impact, potential energy converted into heat energy.
$H e a t p r o d u c e d = l o s s p o t e n t i a l e n e r g y$
$= m g h$
$= 0.2 \times 10 \times 5$
$= 50 \times \frac{2}{10}$
$= 10 J$
The amount of heat produced by the impact is $= 10 \times 2 = 20 J$

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