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7.Gravitation
normal
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