A satellite of mass `m` is circulating around the earth with constant angular velocity. If the radius is `R_(0)` and mass of earth is M, then the angular momentum about the centre of the earth is

Options

A. `M sqrt(GmR_(0))`
B. `m sqrt(GMR_(0))`
C. `m sqrt((R_(0))/(GM))`
D. `M sqrt((Gm)/(R_(0)))`

Answer

B

Explanation

Angular momentum [L = (mv)r]
= linear momentum `xx` perp. Distance between the two
= mass `xx` orbital velocity `xx` radius
`= m sqrt((GM)/(R_(0)))xx R_(0)=m sqrt(GMR_(0))`