Gravitation - Result Question 55

58. The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth’s surface is g. What will be the radius of the orbit of a geostationary satellite?

(a) (R2g/ω2)1/3

(b) (Rg/ω2)1/3

(c) (R2ω2/g)1/3

(d) (R2g/ω)1/3

[1992]

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Answer:

Correct Answer: 58. (a)

Solution:

(a) T=2πrv0=2πr(gR2/r)1/2=2πr3/2gR2=2πω

Hence, r3/2=gR2ω or r3=gR2ω2 or, r=(gR2/ω2)1/3



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