Question

The ratio of accelerations due to gravity \(\mathrm{g}_{1}: \mathrm{g}_{2}\) on the surfaces of two planets is \(5: 2\) and the ratio of their respective average densities \(\rho_{1}: \rho_{2}\) is \(2: 1\). What is the ratio of respective escape velocities \(v_{1}: v_{2}\) from the surface of the planets?
(A) \(5: 2\)
(B) \(\sqrt{5}: \sqrt{2}\)
(C) \(5: 2 \sqrt{2}\)
(D) \(25: 4\)

Answer 1

Ans: (C)
\(: v_{e}=\sqrt{2 g R}, v_{e} \propto \sqrt{g^{2} / \rho}, \frac{v_{1}}{v_{2}}=\sqrt{\frac{25}{8}}=\frac{5}{2 \sqrt{2}}\)

Answer 2

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Answer 3

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