First slide

Gravitaional potential energy

Question

A satellite of mass m is moving in circular orbit around the earth with kinetic energy K and its angular momentum is L. What will be the angular momentum of a satellite of mass 4m which is moving in a circular orbit around the earth with kinetic energy 4K.

Moderate

A

2L
B

4L
C

8L
D

$\frac{L}{2}$

Solution

$\begin{array}{l} Orbital speed v = \sqrt{\frac{GM}{r}} \Rightarrow \frac{GM}{V^{2}} = \frac{GMm}{2 (\frac{1}{2} {mv}^{2})} = \frac{GMm}{2 K} \\ Also, \frac{1}{2} {mv}^{2} = K \Rightarrow V = \sqrt{\frac{2 K}{m}} \\ ∴ L = mVr = m . \sqrt{\frac{2 K}{m}} . \frac{GMm}{2 K} = . \frac{GM}{\sqrt{2 K}} \\ \Rightarrow Lα \frac{{(m)}^{3 / 2}}{{(k)}^{1 / 2}} \Rightarrow \frac{L'}{L} = {(\frac{4 m}{m})}^{3 / 2} {(\frac{k}{4 k})}^{1 / 2} = 4 \end{array}$

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