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Standard XII

Physics

Motion Under Gravity

A body is fal...

Question

A body is falling from height $h$ it takes $t_{1}$ time to reach the ground. The time taken to cover the first half of height is

t_{2} = \frac{t_{1}}{\sqrt{2}}

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t_{2} = \sqrt{2} t_{1}

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t_{2} = \sqrt{3} t_{1}

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none of these

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Solution

The correct option is A $t_{2} = \frac{t_{1}}{\sqrt{2}}$
$h = \frac{1}{2} g t_{1}^{2}$ .... $(1)$
Let time taken to cover the first half of height is $t_{2}$ then $\frac{h}{2} = \frac{1}{2} g t_{2}^{2}$
$h = g t_{2}^{2} . . . . (2)$
from $(1)$ and $(2)$
$\frac{1}{2} g t_{1}^{2} = g t_{2}^{2} \Rightarrow t_{2} = \frac{t_{1}}{\sqrt{2}}$

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