The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth center is increased by eight times to its initial value, then the new angular momentum will be-
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Question

The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth center is increased by eight times to its initial value, then the new angular momentum will be-

Options

G1 Physics · Accepted Answer

For a satellite in a circular orbit, L = mvr and v = √(GM/r) Therefore, L = m√(GMr) So, L ∝ √r The statement says the distance from Earth's centre is increased by eight times its initial value, so r' = r + 8r = 9r Therefore, L'/L = √(9r/r) = 3 Hence, L' = 3L Option B follows.