The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 × 103 km. Find the mass of Mars. Given (4π²)/(G) = 6 × 10¹¹ N⁻¹m⁻²kg² (a) 5.96 × 1019 kg (b) 3.25 × 1021 kg (c) 7.02 × 1025 kg (d) 6.00 × 1023 kg

Answer: (d). T² = (4π² r³)/(GM) ⇒ M = (4π²)/(G)·(r³)/(T²) r = 9.0×10⁶ m, T = 7.5 h = 27000 s = 2.7×10⁴ s M = 6×10¹¹×7.29×10²⁰7.29×10⁸ = 6.00×10²³ kg So the answer is (d).

The planet Mars has two moons, if one of them has a period 7 hours… | JEE Main 2021 (27 Jul, Shift 2)

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Satellites - Orbital Velocity & Period

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $\times$ 103 km. Find the mass of Mars.

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

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Answer: (d)

$T^2 = \frac{4\pi^2 r^3}{GM} \Rightarrow M = \frac{4\pi^2}{G}\cdot\frac{r^3}{T^2}$
$r = 9.0\times10^6$ m, $T = 7.5$ h $= 27000$ s $= 2.7\times10^4$ s
$M = 6\times10^{11}\times\frac{7.29\times10^{20}}{7.29\times10^{8}} = 6.00\times10^{23}$ kg
So the answer is (d).

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