JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Gravitation

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Two satellites A and B having masses in the ratio 4:3 are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is :

(A) $9 : 16$
(B) $16 : 9$ ✓ Correct
(C) $1 : 1$
(D) $4 : 3$

Answer: (B)

Solution

The total mechanical energy of a satellite in circular orbit is

T E = - \frac{GM m}{2 r}

, which is proportional to

\frac{m}{r}

. Given

\frac{m _{1}}{m _{2}} = \frac{4}{3}

and

\frac{r _{1}}{r _{2}} = \frac{3 r}{4 r} = \frac{3}{4}

, we have

\frac{T E _{1}}{T E _{2}} = \frac{m _{1}}{m _{2}} \times \frac{r _{2}}{r _{1}} = \frac{4}{3} \times \frac{4}{3} = \frac{16}{9}

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option

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