Question

Two bodies of masses $m_a$ and $m_b$ are dropped from different heights ${}^{\prime }{a}^{\prime }$ and $‘b^{\prime }$. The ratio of time taken by them to reach the ground is:

• A. $\sqrt{a}:\sqrt{b}$
• B. $a:b$
• C. $1/a:1/b$
• D. $m_a:m_b$

Answer 1

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

The bodies will fall under the action of gravity, therefore from the second equation of motion
For Body A:
$a=ut+\frac{1}{2}g{t}_a^2$
$a=0+\frac{1}{2}g{t}_a^2$
$t_a=\sqrt{\frac{2a}{g}}$
Similaly for body $B$,
$b=0+\frac{1}{2}g{t}_b^2$
Therefore, the ratio of time taken
$t_b=\sqrt{\frac{2b}{g}}$
Therefore, the ratio of time taken
$\frac{t_a}{t_b}=\frac{\sqrt{a}}{\sqrt{b}}$
Therefore, option A is correct.