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A juggler throws balls into the air. He throws one ball whenever the previous one is at its highest point. How high do the balls rise if he throws n balls each second ? Acceleration due to gravity is $g$ .

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$\frac{2 g}{n^{2}}$

$\frac{g}{4 n^{2}}$

$\frac{g}{2 n^{2}}$

$\frac{4 g}{n^{2}}$

answer is C.

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Detailed Solution

Juggler throws $n$ balls in one second so time interval between two consecutive throws is $t = \frac{1}{n} s$

each balls takes $\frac{1}{n} s$ to reach maximum height

So $h_{m a x} = \frac{1}{2} \times g t^{2} = \frac{1}{2} \times g {(\frac{1}{n})}^{2}$

$h_{m a x} = \frac{g}{2 n^{2}}$

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