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Q.

A satellite of mass ‘m’ is in a circular orbit of radius ‘r’ around the earth of mass ‘M’. The additional kinetic energy to be supplied to the satellite, so that it may escape from the orbit is (G = universal gravitational constant)

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a

$\frac{m G M}{r}$

b

$\frac{m G M}{2 r}$

c

$\frac{3 m G M}{2 r}$

d

$\frac{2 m G M}{r}$

answer is B.

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Detailed Solution

Its initial energy in the orbit
$= - \frac{G M m}{2 r}$
To escape a satellite, its total energy must zero.
$- \frac{G M m}{2 r} + K E = O$
$K E = \frac{+ G M m}{2 r}$

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A satellite of mass ‘m’ is in a circular orbit of radius ‘r’ around the earth of mass ‘M’. The additional kinetic energy to be supplied to the satellite, so that it may escape from the orbit is (G = universal gravitational constant)