Question

A balloon rises from rest with a constant acceleration $g / 8$. A stone is relased from it when it has risen to height $h$. The time taken by the stone to reach the ground is

• A. $4 \sqrt{\frac{h}{g}}$
• B. $2 \sqrt{\frac{h}{g}}$
• C. $\sqrt{\frac{2 h}{g}}$
• D. $\sqrt{\frac{g}{h}}$

Answer 1

Answer: (B)

The velocity of balloon at height $h$
$v=\sqrt{2\left(\frac{g}{8}\right) h}$
When the stone released from this balloon. It will go upward with velocity
$v=\frac{\sqrt{g h}}{2}$
In this condition time taken by stone to reach the ground
$t=\frac{v}{g}\left[1+\sqrt{1+\frac{2 g h}{v^{2}}}\right]$
$=\frac{\sqrt{g h} / 2}{g}\left[1+\sqrt{1+\frac{2 g h}{g h / 4}}\right]$
$=\frac{2 \sqrt{g h}}{g}=2 \sqrt{\frac{h}{g}}$