JEE Mains · Physics · STD 11 - 7. gravitation
The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet \(B\) will be:
- A \(\frac{4}{3}\)
- B \(\frac{3}{2}\)
- C \(\frac{2}{3}\)
- D \(\frac{3}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
\(V _{ e }=\sqrt{\frac{2 GM }{ R }}=\sqrt{\frac{2 G \rho \frac{4}{3} \pi R ^{ S }}{ R }}= C \sqrt{\rho} \cdot R\) \(\frac{ V _{ e _1}}{ V _{ e _2}}=\frac{ R _1}{ R _2} \sqrt{\frac{\rho_1}{\rho_2}}=\frac{1}{2}\) \(\frac{ R _1^2}{ R _2^2} \times \frac{\rho_1}{\rho_2}=\frac{1}{4}\)…
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