Question

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. $16:9$
• C. $1:1$
• D. $4:3$

Answer 1

Answer: (B)

Given that $\frac{m_1}{m_2}=\frac{4}{3},\frac{r_1}{r_2}=\frac{3}{4}$
Now $TE=\frac{1}{2}m{v}^2+\left(\frac{-GMm}{r}\right)$
but $\frac{m{v}^2}{r}=\frac{GMm}{r^2}\Rightarrow m{v}^2=\frac{GMm}{r}$
$\Rightarrow TE=-\frac{GMm}{2r}\propto \frac{m}{r}$
$\frac{T{E}_1}{T{E}_2}=\frac{m_1}{m_2}\cdot \frac{r_2}{r_1}=\frac{4}{3}\times \frac{4}{3}=\frac{16}{9}$