A body of mass $5$ kg falls from a height of $20$ metres on the ground and it rebounds to a height of $0.2$ If the loss in Potential energy is used up by the body then what will be the temperature rise? (specific heat of material = $0.09$ cal g $m^{- 1}^{\circ} C^{- 1}$ )

0^{\circ} C

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4^{\circ} C

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8^{\circ} C

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None of these

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Solution

The correct option is D None of these
$E n e r g y l o s t = F i n a l c h a n g e i n P o t e n t i a l E n e r g y (Δ U) = U_{2} - U_{1}; Δ U = m g h_{2} - m g h_{1} = m g (h_{2} - h_{1}) . . . . . . . . . (1) H e a t e n e r g y g a i n e d b y b o d y = m c Δ T, w h e r e c = s p e c i f i c h e a t o f b o d y (C o n v e r t i t t o j o u l e {k g}^{- 1} ℃^{- 1}) m c Δ T = - Δ U . . . . . . . . . . (2) m c Δ T = m g (h_{2} - h_{1}) . . . . . . . . (3) s o l v i n g e q u a t i o n (1) a n d (2) . . . . Δ T = \frac{g (h_{2} - h_{1})}{c} = \frac{10 \times 19.8}{4.2 \times 0.09 \times 1000} = 0.52 ℃$

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