Question

Two bodies of different masses $m_{a}$ and $m_{b}$ are dropped from two different heights $a$ and $b$. The ratio of the time taken by the two to cover these distances are

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

Answer 1

Answer: (C)

$\sqrt{a}:\sqrt{b}$

Answer 2

$h = \frac{1}{2}gt^{2} \Rightarrow t = \sqrt{2h/g}$

$t_{a} = \sqrt{\frac{2a}{g}}\text{and}\mspace{6mu} t_{b} = \sqrt{\frac{2b}{g}} \Rightarrow \frac{t_{a}}{t_{b}} = \sqrt{\frac{a}{b}}$