Two satellites have their masses in the ratio $3:1$ The ratio of the orbit (circular ) are $1:4$ then the ratio of total mechanical energy of A and B

Question

\[(a)\;\frac{12}{1} \quad (b)\;\frac{10}{1} \quad (c)\; \frac{8}{1} \quad (d)\;\frac{5}{1}\]

Answer 1

Energy $E=\large\frac{-GMm}{2r}$

$\large\frac{E_1}{E_2}=\frac{m_1}{r_1} \times \frac{r_2}{m_2}$

$\qquad=\bigg[\large\frac{m_1}{m_2}\bigg]\bigg[\large\frac{r_2}{r_1}\bigg]$

$\qquad=\large\frac{3}{1} \times \frac{4}{1}=\frac{12}{1}$

Hence a is the correct answer.