Question

Two balls are dropped from height $h_1$ and $h_2$ respectively. The ratio of their time of descents is:

• A. $\sqrt{h_2}:\sqrt{h_1}$
• B. $\sqrt{h_1}:\sqrt{h_2}$
• C. $h_2:h_1$
• D. $h_1:h_2$

Answer 1

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

When two balls are dropped from height $h_1$ and $h_2$ respectively, we have,

$h_1=\left(1/2\right)g{t}_1^2$ and $h_2=\left(1/2\right)g{t}_2^2$, where $t_1$ and $t_2$ are respective times.

From these two equations, we get,

$t_1/t_2={\sqrt{h}}_1/{\sqrt{h}}_2$

Therefore the ratio is $t_1:t_2={\sqrt{h}}_1:{\sqrt{h}}_2$