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Question

Physics Question on Escape Speed

There are two planets. The ratio of radius of the two planets is kk but ratio of acceleration due to gravity of both planets is g. What will be the ratio of their escape velocity?

A

(Kg)1/2(Kg)^{1/2}

B

(Kg)−1/2(Kg)^{ - 1/2}

C

(Kg)2(Kg)^{2}

D

(Kg)−2(Kg)^{ - 2}

Answer

(Kg)1/2(Kg)^{1/2}

Explanation

Solution

The equation of escape velocity is ve=2grv _{ e }=\sqrt{2 gr }
so, ve1ve2=2g1r12g2r2=kg\frac{ v _{ e } 1}{ v _{ e } 2}=\frac{\sqrt{2 g _{1} r _{1}}}{\sqrt{2 g _{2} r _{2}}}=\sqrt{ kg }