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Question

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet ? [Given: Mass of planet =8×1022 kg, Radius of planet=2×106 m, Gravitational constant G=6.67×10−11 Nm2/kg2]

A
13
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B
17
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C
11
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D
9
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Solution

The correct option is C 11Given: Height of spaceship =20 km Mass of planet 8×1022 kg Radius of planet=2×106 m, Gravitational constant G=6.67×10−11 Nm2/kg2 Time period of revolution, T=2πrv Velocity of the spaceship, v=√GMr ∴T=2πr√rGM=2π√r3GM Substituting the value, we get T=2π√(202×104)36.67×10−11×8×1022 sec T=7812.2 s T≈2.17 hr ⇒Number of revolutions=242.17≈11. Hence option (D) is correct.

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