Question

A body freely falling from the rest has a velocity $v$ after it falls through a height $h$. The distance, covered by body when it falls down with double of velocity, is :

• A. $ 12\,h $
• B. $ 8\,h $
• C. $ 9\,h $
• D. $ 4\,h $

Answer 1

Answer: (D)

From equation of motion,
we have $ {{v}^{2}}={{u}^{2}}+2\,gh $
where $u$ is initial velocity,
$v$ is final velocity and $h$ is height of fall.
Given, $ u=0 $ (body starts from rest).
$ \therefore $ $ {{v}^{2}}=2\,gh $
Given, $ {{v}_{1}}=v,\,\,{{v}_{2}}=2v,\,{{h}_{1}}=h $
$ \therefore \frac{{{v}_{1}}^{2}}{{{v}_{2}}^{2}}=\frac{2\,g{{h}_{1}}}{2\,g{{h}_{2}}} $
$ \Rightarrow \frac{{{v}^{2}}}{4{{v}^{2}}}=\frac{h}{{{h}_{2}}} $
$ \Rightarrow {{h}_{2}}=4\,h $ .