A satellite of kg mass is revolving in a circular orbit of radius 2R. If energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use g = 10 , R = radius of Earth)

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Solution

Q.
A satellite of $10^{3}$ kg mass is revolving in a circular orbit of radius 2R. If $\frac{10^{4} R}{6} J$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use g = 10 $m / s^{2}$ , R = radius of Earth) [2024]

1 2.5 R

2 3 R

3 4 R

4 6 R

Ans.
(4)

$Total energy = \frac{- G M m}{2 (2 R)}$

$If energy = \frac{10^{4} R}{6} is added then,$

$\frac{- G M m}{4 R} + \frac{10^{4} R}{6} = \frac{- G M m}{2 r}, where r is new radius of revolving$

$- \frac{m g R}{4} + \frac{10^{4} R}{6} = - \frac{m g R^{2}}{2 r}, As g = \frac{G M}{R^{2}}$

$- \frac{10^{3} \times 10 \times R}{4} + \frac{10^{4} R}{6} = - \frac{10^{3} \times 10 \times R^{2}}{2 r}$

$\Rightarrow - \frac{1}{4} + \frac{1}{6} = - \frac{R}{2 r} \Rightarrow r = 6 R$

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