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The radius of a planet is R1 and a sate...

The radius of a planet is `R_1 ` and a satellite revolves round it in a circle of radius `R_2`. The time period of revolution is T. find the acceleration due to the gravitation of the plane at its surface.

Text Solution

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Orbital velocity of the satellite `V_(0) = sqrt(g^(1)R_(2))`
Where `g^(1) = g((R_(1))/(R_(2)))^(2)`
and angular velocity `omega = (V_(0))/(R_(2)) = sqrt((g^(1))/(R_(2))) = sqrt((g(R_(1))^(2))/(R_(2)^(3)))`
But time period of revolution `T = (2pi)/(omega) = 2pisqrt((R_(2)^(3))/(gR_(1)^(2)))`
(or) `T^(2) = 4pi^(2)(R_(2)^(3))/(gR_(1)^(2))` (or) `g = (4pi^(2))/(T^(2)) (R_(2)^(3))/(R_(1)^(2))`
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