JEE Mains · Physics · STD 11 - 7. gravitation
Two planets \(A\) and \(B\) having masses \(m_1\) and \(m_2\) move around the sun in circular orbits of \(r_1\) and \(r_2\) radii respectively. If angular momentum of \(\mathrm{A}\) is \(\mathrm{L}\) and that of \(B\) is \(3L\), the ratio of time period \(\left(\frac{T_A}{T_B}\right)\) is _______.
- A \(\left(\frac{r_2}{r_1}\right)^{\frac{3}{2}}\)
- B \(\left(\frac{r_1}{r_2}\right)^3\)
- C \(\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3\)
- D \(27\left(\frac{m_1}{m_2}\right)^3\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{27}\left(\frac{m_2}{m_1}\right)^3\)
Step-by-step Solution
Detailed explanation
\(\frac{\pi \mathrm{r}_1^2}{\mathrm{~T}_{\mathrm{A}}}=\frac{\mathrm{L}}{2 \mathrm{~m}_1} \ldots \ldots . .(1)\) \(\frac{\pi \mathrm{r}_2^2}{\mathrm{~T}_{\mathrm{B}}}=\frac{3 \mathrm{~L}}{2 \mathrm{~m}_2} \ldots \ldots .(2)\)…
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