MHT CET · Physics · Rotational Motion
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 \(\mathrm{m}(\mathrm{GMr})\)
- B \(\mathrm{m}(\mathrm{GMr})^{1 / 2}\)
- C \((\mathrm{GMmr})^{1 / 2}\)
- D \(\left(\frac{\mathrm{GMr}}{\mathrm{m}}\right)^{2}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{m}(\mathrm{GMr})^{1 / 2}\)
Step-by-step Solution
Detailed explanation
Angular momentum \(=m v r=m \sqrt{\frac{G M}{r}} r \)
\( =m \sqrt{G M r} \)
\( =m(G M r)^{\frac{1}{2}}\)
\( =m \sqrt{G M r} \)
\( =m(G M r)^{\frac{1}{2}}\)
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