Gujarati
Hindi
7.Gravitation
normal

A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

A

$gR$

B

$\sqrt {gR} $

C

$\sqrt {g/R} $

D

$g/R$

Solution

according to conservation of energy

$\frac{-\mathrm{GMm}}{2 \mathrm{R}}+0=-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$

$\Rightarrow \frac{\mathrm{GMm}}{2 \mathrm{R}}=\frac{1}{2} \mathrm{mv}^{2} \Rightarrow \mathrm{v}^{2}=\frac{\mathrm{GM}}{\mathrm{R}}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \times \mathrm{R}$

$\Rightarrow \quad \mathrm{v}=\sqrt{\mathrm{gR}}$

Standard 11
Physics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.