Question

A satellite of mass ‘m’ is revolving around the earth of mass ‘M’ in an orbit of radius ‘r’. The angular momentum of the satellite about the centre of orbit will be

• A. $\sqrt {GMmr}$
• B. $\sqrt {GMm^2r}$
• C. $\sqrt {mvr}$
• D. $\sqrt {GMm}$

Answer 1

The Correct Option is B

The angular momentum (L) of a satellite revolving around a central body can be calculated using the formula: 
L = mvr 
To find the linear velocity (v) of the satellite, we can use the gravitational force equation: 
$\frac {GMm}{r^2}$ = $\frac {mv^2}{r}$
Rearranging the equation, we can find the value of v: 
v = $\sqrt {\frac {GM}{r}}$
Substituting this value of v back into the formula for angular momentum: 
L = $m(\sqrt {\frac {GM}{r}})r$ 
L = $\sqrt {GMm^2r}$
Therefore, the correct answer is (B) $\sqrt {GMm^2r}$ for the angular momentum of the satellite about the center of the orbit.