Question

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights, viz $a$ and $b$. The ratio of time taken by both bodies to reach the ground 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 $\sqrt{a}:\sqrt{b}$

Acceleration due to gravity acting on both the bodies is same i.e. $g$.

Initial speed of the bodies $u=0$

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

Thus we get $S=\frac{1}{2}g{t}^2$

Or $t=\sqrt{\frac{2S}{g}}$

$⟹$ $t\propto \sqrt{S}$

Thus $\frac{t_a}{t_b}=\sqrt{\frac{a}{b}}$