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Question 70 of 88

Q.For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is :

(a) 2
(b) sqrt(2)
(c) 1/2
(d) 1/sqrt(2)
Puducherry TnboardTamil Nadu HSC First Year (DGE) Board 2019MCQ· 1mImportance★★★★★
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For any satellite in a circular orbit, KE/|PE| = 1/2.

For a satellite of mass m orbiting a planet of mass M at radius r:

Gravitational potential energy: PE = -GMm/r

Orbital speed is found from the centripetal force condition: GMm/r^2 = mv^2/r, so v^2 = GM/r

Kinetic energy: KE = (1/2)mv^2 = (1/2)m(GM/r) = GMm/(2r)

Ratio of kinetic energy to potential energy (taking magnitudes, since PE is negative):

KE/|PE| = [GMm/(2r)] / [GMm/r] = 1/2 …

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