Question

A body is dropped from a height $h$. If $t_1$ and $t_2$ be the times in covering first half and the next half distances respectively, then the relation between $t_1$ and $t_2$ is

• A. $t_1 = t_2$
• B. $t_1 = 2t_2$
• C. $t_1 = 3t_2$
• D. $t_1 = \frac{t_2}{(\sqrt{2} - 1)}$

Answer 1

Answer: (D)

$t_{1} = \sqrt{\frac{2\left(h/2\right)}{g}} = \sqrt{\frac{h}{g}}$
$\Rightarrow t_{1}+t_{2} = \sqrt{\frac{2h}{g}} $
$\Rightarrow t_{2} =\sqrt{\frac{2h}{g}} -t_{1} = \left(\sqrt{2} -1\right)\sqrt{\frac{h}{g}}$
$\Rightarrow \frac{t_{1}}{t_{2}} = \frac{1}{\sqrt{2}-1} $
$ \Rightarrow \frac{t_{2}}{\sqrt{2}-1}$