Q104 / 150 · MHT CET 2020 (19 Oct Shift 1) · Physics

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)

  • A
    $\mathrm{m}(\mathrm{GMr})$
  • Correct answer
    B
    $\mathrm{m}(\mathrm{GMr})^{1 / 2}$
  • C
    $(\mathrm{GMmr})^{1 / 2}$
  • D
    $\left(\frac{\mathrm{GMr}}{\mathrm{m}}\right)^{2}$

Solution

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

Hence, the correct answer is option: 'B'.

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