Question

A body when released from the top of a tower of height $h$ reaches the ground in time 1 second. Time in second at which it is a height $\frac{h}{2}$ above the groun.d is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2}}$

Answer 2

Here, $h = \frac{1}{2} gt^2$
$2h = g$ $( \because \:\: t = 1 s)$
Let $t'$ = time at which body is at height $\frac{h}{2}$
$\therefore \:\:\: \frac{h}{2} = \frac{1}{2} gt'^2$ or , \frac{1}{2} \frac{2h}{g} = t' ^2 or $t'^2 = \frac{1}{2}$
$\therefore \:\:\: t' = \frac{1}{\sqrt{2}}s$