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Two satellites $\mathrm{A\: and\: B}$ having masses in the ratio $\mathrm{ 4: 3, }$ are revolving in circular orbits of radii $\mathrm{ 3 \mathrm{r}}$ and $\mathrm{ 4 \mathrm{r}}$ respectively around the earth. The ratio of total mechanical energy of $\mathrm{ A}$ to $\mathrm{ B}$ is:
Option: 1
$9: 16$

Option: 2
$16: 9$

Option: 3
$1: 1$

Option: 4
$4: 3$

Answers (1)

best_answer

Total mechanical energy is $\mathrm{T E=-\frac{P E}{2}}$
for satellite 1 ,

$\mathrm{ T E_1=\frac{-G M m_1}{2(3 r)} }$

For satellite 2,

$\mathrm{T E_2=\frac{-G M m_2}{2(4r)} }$

$\mathrm{\frac{T E_1}{T E_2}=\frac{8 m_1}{6 m_2}=\frac{4}{3} \times \frac{4}{3}=\frac{16}{9}}$

Hence 2 is correct option.

Posted by

himanshu.meshram

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