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 the two to drop through these distances is

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

Answer 1

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

Since, the bodies are dropped, $u=0$
From equation of motion we have,
$S=ut+\frac{1}{2}a{t}^2$
$\Rightarrow -h=0+\frac{1}{2}(-g)t^2$
$\Rightarrow t=\sqrt{\frac{2h}{g}}$
Now from above equation we can say
$t\propto \sqrt{h}$
$\Rightarrow \frac{t_a}{t_b}=\frac{\sqrt{a}}{\sqrt{b}}$