Radius of earth is R . If a body is taken to a height 3R from surface of earth than change in potent

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7.Gravitation

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Radius of the earth is $R$. If a body is taken to a height $3R$ from the surface of the earth than change in potential energy will be

A

$3mgR$

B

$\frac {3}{2}\,mgR$

C

$mgR$

D

$\frac {3}{4}\,mgR$

Solution

$\Delta \mathrm{U}=\mathrm{U}_{\mathrm{f}}-\mathrm{U}_{\mathrm{i}}=-\frac{\mathrm{GMm}}{4 \mathrm{R}}-\left(-\frac{\mathrm{GMm}}{\mathrm{R}}\right)$

$\Delta \mathrm{U}=\frac{\mathrm{GMm}}{\mathrm{R}}-\frac{\mathrm{GMm}}{4 \mathrm{R}}=\frac{3}{4} \frac{\mathrm{GMm}}{\mathrm{R}}$

$\quad=\frac{3}{4} \mathrm{Mg} \mathrm{R}$

Standard 11

Physics

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