Question

A body thrown vertically up reaches a maximum height of 50 m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of :

• A. 100 m
• B. 200 m
• C. 400 m
• D. 50 m

Answer 1

The correct option is B 200 m

If $u$ be the initial velocity of a body and $h$ be the maximum height, then by energy conservation, $\frac{1}{2}m{u}^2=mgh$ or $u=\sqrt{2gh}$

In second case, if $h^{\prime }$ be the maximum height, initial velocity $u^{\prime }=\sqrt{2g{h}^{\prime }}$

Given, $u^{\prime }=2u$ or $\sqrt{2g{h}^{\prime }}=2\sqrt{2gh}$ or $h^{\prime }=4h=4\times 50=200m$ (as given $h=50m$)