Question

A body, thrown upwards with some velocity reaches the 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. 300 m
• D. 400 m

Answer 1

Answer: (B)

At maximum height, final velocity is zero.
From equation of motion, we have
$v^{2}=u^{2}-2 g h$
Where $v$ is final velocity, $u$ is initial velocity, $h$ is height and $g$ is acceleration due to gravity.
Since body reaches maximum height in both cases, hence final velocity is zero.
$\therefore v=0 $
$\Rightarrow \frac{h_{1}}{h_{2}}=\frac{u_{1}^{2}}{u_{2}^{2}}$
Given, $ u_{2}=2 u_{1}, v_{1}=u$
$\therefore \frac{h_{1}}{h_{2}}=\frac{u^{2}}{(2 u)^{2}}=\frac{1}{4}$
$\Rightarrow h_{2}=4 h_{1}=4 \times 50$
$=200\, m $.
Note: Maximum height attained does not depend upon the mass of the body.