Question

Two balls of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b$. The ratio of time taken by the two to drop through these distances is

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

Answer 1

The correct option is D $a^2:b^2$

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 $S=ut+\frac{1}{2}\times a{t}^2$

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

⟹ $t\propto \sqrt{S}$
Thus $\frac{t_a}{t_b}=\frac{\sqrt{a}}{\sqrt{b}}$
For detailed solution please watch the next video.