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 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
Updated On: May 12, 2024
- $ \frac{1}{2}$
- $ \frac{1}{4}$
- $ \frac{1}{\sqrt{2}}$
- $ \frac{1}{\sqrt{3}}$
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The Correct Option is C
Solution and Explanation
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$
$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$
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.