Question

A satellite of mass '$m$' is revolving in circular orbit of radius '$r$' round the earth. Its angular momentum with respect to the center of its orbit is ($M=$ mass of earth, $G=$ universal gravitational constant)

• A. ${\left(GMmr\right)}^{\frac{1}{2}}$
• B. ${\left(GM{m}^{2}r\right)}^{\frac{1}{2}}$
• C. ${\left(GM{m}^2{r}^2\right)}^{\frac{1}{2}}$
• D. ${\left(G{M}^2{m}^{2}r\right)}^{\frac{1}{2}}$

Answer 1

Answer: (B)

${\left(GM{m}^{2}r\right)}^{\frac{1}{2}}$

Centrifugal force acting on the satellite is balanced by the gravitational force due to earth on satellite.

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

We get $v=(\frac{GM}{r}{)}^{1/2}$

Angular momentum of satellite $L=mvr$

$\therefore$ $L=m(\frac{GM}{r}{)}^{1/2}r$

$⟹$ $L=(GM{m}^{2}r{)}^{1/2}$