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Dropping Objects

Two bodies of...

Question

Two bodies of different masses $m_{a}$ and $m_{b}$ are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distances are

a:b

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b:a

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$\sqrt{a} : \sqrt{b}$

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$a^{2} : b^{2}$

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Solution

The correct option is C
$\sqrt{a} : \sqrt{b}$

We have, in general

$h = \frac{1}{2} g t^{2} \Rightarrow t = \sqrt{\frac{2 h}{g}}$

For the two bodies in question, we have

$t_{a} = \sqrt{\frac{2 a}{g}}$ and $t_{b} = \sqrt{\frac{2 b}{g}} \Rightarrow \frac{t_{a}}{t_{b}} = \sqrt{\frac{a}{b}}$

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The correct option is C
$\sqrt{a} : \sqrt{b}$

We have, in general

$h = \frac{1}{2} g t^{2} \Rightarrow t = \sqrt{\frac{2 h}{g}}$

For the two bodies in question, we have

$t_{a} = \sqrt{\frac{2 a}{g}}$ and $t_{b} = \sqrt{\frac{2 b}{g}} \Rightarrow \frac{t_{a}}{t_{b}} = \sqrt{\frac{a}{b}}$