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A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth; the orbital speed of the satellite is (a) gR 2 /R+ x (b) gR / R- x (c) gx (d) (gR 2 /R+x) 1/2

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth; the orbital speed of the satellite is
 
(a) gR2/R+ x
(b) gR / R- x
(c) gx
(d) (gR2/R+x)1/2

Grade:6

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago

. (d) Gravitational force provides the necessary centripetal force.

? mv2/(R+x) = GmM / (R+x)2 also g = GM /R2

? mv2/( R+x ) = m (GM/R2) R2/( R + x )2

? v2 = gR2/R+x ? v = (gR2 / R+x )1/2

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