A satellite of mass is revolving around earth in a circular orbit at a height of from earth surfae. The angular momentum of the satellite is . The value of x is ________, where M and R are the mass and radius of earth, respectively. (G is the gravitatio

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Solution

Q.
A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$ . The value of x is ________, where M and R are the mass and radius of earth, respectively. (G is the gravitational constant) [2025]

Ans.
(3)

(i) If earth is assumed to be stationary

Orbital velocity $v_{0} = \sqrt{\frac{G M}{4 R / 3}} = \sqrt{\frac{3 G M}{4 R}}$

Angular momentum of satellite

$L = \frac{M}{2} v_{0} \frac{4 R}{3}$

$L = \frac{M}{2} \cdot \sqrt{\frac{3 G M}{4 R}} \cdot \frac{4 R}{3} = M \sqrt{\frac{G M R}{3}}$

$\Rightarrow x = 3$

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