MHT CET · Physics · Rotational Motion
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 \(\sqrt{\mathrm{R}}\)
- D \(\mathrm{R}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\mathrm{R}}\)
Step-by-step Solution
Detailed explanation
Angular momentum of the earth,
\(\mathrm{L}=\mathrm{mVR} \quad \text { but } \quad \mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}\)
where \(M\) is the mass of the sun
\(\begin{array}{l}
\therefore L=m R \sqrt{\frac{G M}{R}}=m \sqrt{G M R} \\
\therefore L \propto \sqrt{R}
\end{array}\)
\(\mathrm{L}=\mathrm{mVR} \quad \text { but } \quad \mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}\)
where \(M\) is the mass of the sun
\(\begin{array}{l}
\therefore L=m R \sqrt{\frac{G M}{R}}=m \sqrt{G M R} \\
\therefore L \propto \sqrt{R}
\end{array}\)
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