Time taken by an object falling from rest to cover the heights of $h_{1}$ and $h_{2}$ are respectively $t_{1}$ and $t_{2}$ . Then the ratio of $t_{1}$ to $t_{2}$ is

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{2h}_{1} : h_{2}

h_{1} : h_{2}

\sqrt{h_{1}} : \sqrt{h_{2}}

h_{1} : 2 h_{1}

answer is B.

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Detailed Solution

Initial velocity u = 0

$S = ut + \frac{1}{2} {at}^{2} \Rightarrow S = \frac{1}{2} {at}^{2} \Rightarrow S α t^{2}$

$\Rightarrow \frac{h_{1}}{h_{2}} = \frac{t_{1}^{2}}{t_{2}^{2}} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{\sqrt{h_{1}}}{\sqrt{h_{2}}}$

$t_{1} : t_{2} = \sqrt{h_{1}} : \sqrt{h_{2}}$

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