Q 11-07-073JEE MainJEE Main 2024 (9 Apr, Shift 2)Medium
A satellite of $10^3\ \text{kg}$ mass is revolving in a circular orbit of radius $2R$. If $\dfrac{10^4R}{6}\ \text{J}$ 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):
Answer: (D) $6R$
Total energy in a circular orbit of radius $r$: $E = -\dfrac{GMm}{2r} = -\dfrac{gR^2m}{2r}$.
$$\Delta E = \frac{gR^2m}{2}\left(\frac{1}{2R} - \frac1r\right) = 10^4R\left(\frac14 - \frac{R}{2r}\right)$$
Setting this equal to $\dfrac{10^4R}{6}$:
$$\frac14 - \frac{R}{2r} = \frac16 \;\Rightarrow\; \frac{R}{2r} = \frac1{12} \;\Rightarrow\; r = 6R$$
Solution by Sreeraj P, M.Sc Physics