MHT CET · Physics · Motion In Two Dimensions
Earth revolves round the sun in a circular orbit of radius 'R'. The angular momentum of the revolving earth is directly proportional to
- A \(\mathrm{R}^{2}\)
- B \(\mathrm{R}^{3}\)
- C \(\mathrm{R}\)
- D \(\sqrt{\mathrm{R}}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{\mathrm{R}}\)
Step-by-step Solution
Detailed explanation
Correct option is A)
We know that angular momentum of Earth
\(\begin{array}{l}\mathrm{L}=\mathrm{mvR} \\\Rightarrow \mathrm{L}=\mathrm{m} \sqrt{\frac{\mathrm{GM}}{\mathrm{R}}} \times \mathrm{R} \\\Rightarrow \mathrm{L} \propto \mathrm{R}^{1 / 2}\end{array}\)
We know that angular momentum of Earth
\(\begin{array}{l}\mathrm{L}=\mathrm{mvR} \\\Rightarrow \mathrm{L}=\mathrm{m} \sqrt{\frac{\mathrm{GM}}{\mathrm{R}}} \times \mathrm{R} \\\Rightarrow \mathrm{L} \propto \mathrm{R}^{1 / 2}\end{array}\)
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