JEE Mains · Physics · STD 11 - 7. gravitation
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 \(6.00 \times 10^{23} \,{kg}\)
Answer & Solution
Correct Answer
(D) \(6.00 \times 10^{23} \,{kg}\)
Step-by-step Solution
Detailed explanation
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 \({M}=6 \times 10^{23}\)
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