Question

Two balls are dropped from heights $h_1$ and $h_2$ respectively. The ratio of their velocities on reaching the ground is __________ .

• A. $\sqrt{h_1}:\sqrt{h_2}$
• B. $h_1:h_2$
• C. $h_1^2:h_2^2$
• D. none of these

Answer 1

The correct option is A $\sqrt{h_1}:\sqrt{h_2}$

Initial velocity of ball

$u=0$

Let the final velocity on reaching the ground be $v$

Using 3rd equation of motion-

$v^2=u^2+2gh$

$\Rightarrow v^2=0+2gh$

$\Rightarrow v=\sqrt{2gh}$

We get

$v\propto \sqrt{h}$

$\Rightarrow v_1:v_2=\sqrt{h_1}:\sqrt{h_2}$