Planet Mars has two moons, if one of them has a period 7, hours,, 30, minutes and an orbital radius

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7.Gravitation

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The planet Mars has two moons, if one of them has a period $7\, hours,\, 30\, minutes$ and an orbital radius of $9.0 \times 10^{3}\, {km} .$ Find the mass of Mars.

$\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}$

A

$3.25 \times 10^{21}\, {kg}$

B

$5.96 \times 10^{19} \,{kg}$

C

$7.02 \times 10^{25} \,{kg}$

D

$6.00 \times 10^{23} \,{kg}$

(JEE MAIN-2021)

Solution

Using kepler's law

$T^{2}=\frac{4 \pi^{2}}{G M} \cdot r^{3}$

$M=\frac{4 \pi^{2}}{G} \cdot \frac{r^{3}}{T^{2}}$

by putting values

${M}=6 \times 10^{23}$

Standard 11

Physics

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