A body of mass $3 k g$ falls from the multi-storeyed building $100 m$ high and buries itself $2 m$ deep in the sand. The time of penetration is

9 s e c

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0.9 s e c

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0.09 s e c

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10 s e c

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Solution

The correct option is D $0.09 s e c$
$V = \sqrt{2 g H} = \sqrt{2000} m / s v^{2} - u^{2} = 2 a s \Rightarrow 0 - 2000 = 2 \times a \times 2 \Rightarrow a = - 500 m / s^{2} v = u + a t \Rightarrow t = \frac{\sqrt{2000}}{500} = 0.089 s \sim 0.09 s$

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A stone of mass 5 kg falls from the top of a 50 m high building and penetrates 1 m deep in the sand. Find the time taken to penetrate.

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