- Home
- Standard 11
- Physics
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
$\frac{-\mathrm{GMm}}{2 \mathrm{R}}+0=-\frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mv}^{2}$
$\Rightarrow \frac{\mathrm{GMm}}{2 \mathrm{R}}=\frac{1}{2} \mathrm{mv}^{2} \Rightarrow \mathrm{v}^{2}=\frac{\mathrm{GM}}{\mathrm{R}}=\frac{\mathrm{GM}}{\mathrm{R}^{2}} \times \mathrm{R}$
$\Rightarrow \quad v=\sqrt{g R}$
Standard 11
Physics
