MHT CET · Physics · Gravitation

A satellite of mass \(m\) is moving in a circular orbit of radius \(r\) around the earth. The angular momentum of the satellite about the center of orbitis ( \(M=\) mass of earth, \(G=\) gravitational constant)

A \(\left(G M m^2 r^2\right)^{1 / 2}\)
B \((G M m r)\)
C \(\left(G M m^2 r\right)^{1 / 2}\)
D \(\left(G M^2 m r\right)^{1 / 2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(G M m^2 r\right)^{1 / 2}\)

Step-by-step Solution

Detailed explanation

Let the satellite revolves in a circular orbit of radius \(r\) with a linear velocity \(v\).
The centripetal force of acting on the satellite is balanced by the gravitational force due to the earth.
\(\begin{aligned} & \therefore F_{\text {centripetal }}=F_{\text {gravitational }} \\ & \Rightarrow \frac{m v^2}{r}=\frac{G M m}{r^2} \\ & \Rightarrow v=\sqrt{\frac{G M}{r}}\end{aligned}\)
Angular momentum of satellite about the center of orbit, is
\(L=m v r=m\left(\frac{G M}{r}\right)^{1 / 2} r=\left(G M m^2 r\right)^{1 / 2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app