Question

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights, $a$ and $b$ respectively. The ratio of times taken by the two to drop through these distances is:

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

Answer 1

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

As we know that, time taken by the body after dropping to reach the certain depth is given as
$t=\sqrt{\frac{2h}{g}}$, where, $h$ is the height from where body is dropped.
$\therefore$ For height $a$:
$t_1=\sqrt{\frac{2a}{g}}$
And for height $b$:
$t_2=\sqrt{\frac{2b}{g}}$
Thus, $\frac{t_1}{t_2}=\frac{\sqrt{a}}{\sqrt{b}}$