Two satellites $A$ and $B$ having ratio of masses $3: 1$ are revolving in circular orbits of radii ' $r$ '…

Two satellites $A$ and $B$ having ratio of masses $3: 1$ are revolving in circular orbits of radii ' $r$ ' and ' 4 r '. The ratio of total energy of satellites A to that of $B$ is
  1. $1: 3$
  2. $3: 1$
  3. $3: 4$
  4. $12: 1$

Solution

$\begin{aligned} \frac{E_A}{E_B} & =\frac{M_A}{M_B} \times \frac{r_B}{r_A} \quad \ldots\left(E \propto \frac{M}{r}\right) \\ & =\frac{3}{1} \times \frac{4 r}{r} \\ \frac{E_A}{E_B} & =\frac{12}{1}\end{aligned}$

Asked in: MHT CET 2024 (09 May Shift 1)

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