A particle is kept at rest at a distance 'R' from surface of earth (of radius R ). minimum s

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7.Gravitation

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A particle is kept at rest at a distance $'R'$ from the surface of earth (of radius $R$). The minimum speed with which it should be projected so that it does not return is

A

$\sqrt {\frac{{GM}}{{4R}}} $

B

$\sqrt {\frac{{GM}}{{2R}}} $

C

$\sqrt {\frac{{GM}}{{R}}} $

D

$\sqrt {\frac{{2GM}}{{R}}} $

Solution

As $\mathrm{Ve}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{r}}} \quad$ here $\mathrm{r}=2 \mathrm{R}$

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

Standard 11

Physics

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