A satellite of 10³ kg mass is revolving in circular orbit of radius… | JEE Main 2024 (9 Apr, Shift 2)

Q12JEE Main 2024 · 9 APR · SHIFT 2Medium

Satellite Energy & Weightlessness

A satellite of $10^{3}\text{ kg}$ mass is revolving in circular orbit of radius $2R$ . If $\frac{10^{4}R}{6}\text{ J}$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius

(use $g = 10\text{ m/s}^{2}, R =$ radius of earth)

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Answer: (b)

With $GM = gR^2$ : $E = -\frac{GMm}{2r} = -\frac{mgR^2}{2r}$ .
Initial ( $r = 2R$ ): $E_i = -\frac{mgR}{4}$ . Energy given $\frac{10^4R}{6} = \frac{mgR}{6}$ (since $mg = 10^4$ N).
$E_f = -\frac{mgR}{4} + \frac{mgR}{6} = -\frac{mgR}{12}$ .
$-\frac{mgR^2}{2r} = -\frac{mgR}{12} \Rightarrow r = 6R$ .
So the answer is (b) $6R$ .

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