A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant…

A satellite of mass 'm' is revolving around the earth of mass 'M' in an orbit of radius 'r' with constant angular velocity ' $\omega^{\prime}$. The angular momentum of the satellite is (G = gravitational constant)
  1. $\mathrm{m}(\mathrm{GMr})$
  2. $\mathrm{m}(\mathrm{GMr})^{1 / 2}$
  3. $(\mathrm{GMmr})^{1 / 2}$
  4. $\left(\frac{\mathrm{GMr}}{\mathrm{m}}\right)^{2}$

Solution

$\begin{aligned} \text {Angular momentum } &=m v r=m \sqrt{\frac{G M}{r}} r \\ &=m \sqrt{G M r} \\ &=m(G M r)^{\frac{1}{2}} \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 1)

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