Given that mass of earth is M and its radius is R . A body is dropped from a height equal to radius

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7.Gravitation

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Given that mass of the earth is $M$ and its radius is $R$. A body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground its velocity will be

A

$\left[ {\frac{{GM}}{R}} \right]$

B

${\left[ {\frac{{GM}}{R}} \right]^{1/2}}$

C

${\left[ {\frac{{2GM}}{R}} \right]^{1/2}}$

D

$\left[ {\frac{{2GM}}{R}} \right]$

Solution

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

$\Rightarrow \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$

Standard 11

Physics

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