Escape velocity from a planet is Vₑ. A tunnel is dug along diameter of planet and a small b

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7.Gravitation

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The escape velocity from a planet is $V_e.$ A tunnel is dug along the diameter of the planet and a small body dropped into it. The speed of the body at the centre of the planet will be

A

$\frac {V_e}{\sqrt 2}$

B

$\frac {V_e}{2}$

C

$V_e$

D

$2V_e$

Solution

Energy conservation

$-\frac{\mathrm{GMm}}{\mathrm{R}}+0=-\frac{3}{2} \frac{\mathrm{GMm}}{\mathrm{R}}+\frac{1}{2} \mathrm{mV}^{2}$

$\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$ so $\mathrm{V}=\frac{\mathrm{V}_{\mathrm{e}}}{\sqrt{2}}$

Standard 11

Physics

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