MCQ
Two satellites $A$ and $B$ having masses in the ratio $4: 3$ are revolving in circular orbits of radii $3\,r$ and $4\,r$ respectively around the earth. The ratio of total mechanical energy of $A$ to $B$ is.
- A$9: 16$
- ✓$16: 9$
- C$1: 1$
- D$4: 3$
✓
Answer
Correct option: B.
$16: 9$
b
Given that $\frac{m_{1}}{m_{2}}=\frac{4}{3}, \frac{r_{1}}{r_{2}}=\frac{3}{4}$
Given that $\frac{m_{1}}{m_{2}}=\frac{4}{3}, \frac{r_{1}}{r_{2}}=\frac{3}{4}$
Now $T E=\frac{1}{2} mv ^{2}+\left(\frac{- GMm }{ r }\right)$
but $\frac{ mv ^{2}}{ r }=\frac{ GMm }{ r ^{2}} \Rightarrow mv ^{2}=\frac{ GMm }{ r }$
$\Rightarrow TE =-\frac{ GMm }{2 r } \propto \frac{ m }{ r }$
$\frac{T E_{1}}{T_{2}}=\frac{m_{1}}{m_{2}} \cdot \frac{r_{2}}{r_{1}}=\frac{4}{3} \times \frac{4}{3}=\frac{16}{9}$
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