Question

The bodies of different masses $m_a$ and $m_b$ are dropped from two different heights i.e., a and b. The ratio of time taken by both bodies to drop through these distance is :

• A. $\sqrt{a}:\sqrt{b}$
• B. $\frac{m_a}{m_b}:\frac{b}{a}$
• C. a : b
• D. $a^2:b^2$

Answer 1

The correct option is A $\sqrt{a}:\sqrt{b}$

Initial speed of the bodies $u=0$

Distance covered by a body in time $t$, $S=ut+\frac{1}{2}g{t}^2$

Or $S=0+\frac{g}{2}{t}^2$

So, $t=\sqrt{\frac{2S}{g}}$

Given : $S_1=a$ and $S_2=b$

$⟹$ $t_1:t_2=\sqrt{S_1}:\sqrt{S_2}=\sqrt{a}:\sqrt{b}$