Question

If two bodies of different masses $m_1$ and $m_2$ are dropped from different heights $h_1$ and $h_2$, then ratio of the times taken by the two to drop through these distances is

• A. $h_1:h_2$
• B. $h_2/h_1$
• C. $\sqrt{h_1}:\sqrt{h_2}$
• D. $h_1^2:h_2^2$

Answer 1

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

Distance fallen by a freely body,
$\Rightarrow s=\frac{1}{2}{gt}^2$
$s\propto t^2....[\because \frac{1}{2}gisconstant]$
$\therefore \frac{s_1}{s_2}=\frac{t_1^2}{t_2^2}$
$\Rightarrow \frac{h_1}{h_2}=\frac{t_1^2}{t_2^2}$
$\Rightarrow \frac{t_1}{t_2}=\sqrt{\frac{h_1}{h_2}}$