Q. A satellite of mass $\frac M2$ is revolving around earth in a circular orbit at a height of $\frac R3$ from earth surface. The angular momentum of the satellite is $M\sqrt{\frac{GMR}x}$. The value of $x$ is ______, where $M$ and $R$ are the mass and radius of earth, respectively. ( G is the gravitational constant)
Numerical Question
This is a numerical-answer question. The correct answer is shown below.
Explanation
[Solution by Dr. Abubacker] The orbital radius is $r=R+\frac R3=\frac{4R}3$. $L=mvr=m\sqrt{GMr}=\frac M2\sqrt{GM\cdot\frac{4R}3}=M\sqrt{\frac{GMR}3}$, so $x=3$. Answer: 3.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.