A satellite is revolving round earth with orbital speed v_0 . If it stops suddenly, speed with which

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7.Gravitation

hard

A satellite is revolving round the earth with orbital speed $v_0$. If it stops suddenly, the speed with which it will strike the surface of earth would be : ($v_e =$ escape velocity of a particle on earth's surface)

A

$\frac{{v_e^2}}{{{v_0}}}$

B

$v_0$

C

$\sqrt {v_e^2 - v_0^2} $

D

$\sqrt {v_e^2 - 2v_0^2} $

Solution

By energy conservation

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

$v^{2}=\frac{2 G M}{R}-\frac{2 G M}{r}=v_{e}^{2}-2 v_{0}^{2}$

$\Rightarrow v=\sqrt{v_{e}^{2}-2 v_{0}^{2}}$

Standard 11

Physics

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