Question

Two planets of mass m₁ and m₂ are revolving around their sun in radius of their orbits r₁ and r₂ respectively. Angular momentum of planets are in ratio of 3 then \(\frac{T_1}{T_2}\) is (T₁ and T₂ are periods of revolutions)

(1) \(27(\frac{m_2}{m_1})^3\) 

(2) \(\frac{1}{27}(\frac{m_2}{m_1})^3\) 

(3) \((\frac{r_1}{r_2})^3\) 

(4) \((\frac{r_2}{r_1})^{3/2}\)

Answer 1

Correct Option is (2)  \(\frac{1}{27}(\frac{m_2}{m_1})^3\) 

 

\(\frac{m_2}{3m_1}= (\frac{T_1}{T_2})^{1/3}\) 

\(\frac{T_1}{T_2}= \frac{1}{27}(\frac{m_2}{m_1})^3\)