Question:
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0 \times 10^{3} \mathrm{~km}$. Find the mass of Mars.
$\left\{\operatorname{Given} \frac{4 \pi^{2}}{\mathrm{G}}=6 \times 10^{11} \mathrm{~N}^{-1} \mathrm{~m}^{-2} \mathrm{~kg}^{2}\right\}$
Correct Option: , 4
Solution:
Option D is correct
$\mathrm{T}^{2}=\frac{4 \pi^{2}}{\mathrm{GM}} \cdot \mathrm{r}^{3}$
$\mathrm{M}=\frac{4 \pi^{2}}{\mathrm{G}} \cdot \frac{\mathrm{r}^{3}}{\mathrm{~T}^{2}}$
by putting values
$M=6 \times 10^{23}$
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