A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 and mass of the earth M , the angular momentum about the center of the earth is

Q: A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R0 and mass of the earth M , the angular momentum about the center of the earth is

(a) $m \sqrt{G M R_0} $

(b) $ m \sqrt{G m R_0} $

(c) $ m \sqrt{\frac{G M}{R_0}} $

(d) $ M \sqrt{\frac{G m}{R_0}} $

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Ans: (a)
Sol: L = m v r

$\displaystyle L = m \sqrt{\frac{G M}{R_0} } \; R_0$

$\displaystyle L = \sqrt{G M R_0}$