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Question

Physics Question on Escape Speed

The escape velocity from the Earth's surface is vv. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

A

v

B

2 v

C

3 v

D

4 v

Answer

4 v

Explanation

Solution

Ve=2GMR=2G43πR3ρRV_{e}=\sqrt{\frac{2 G M}{R}}=\sqrt{\frac{2 G \frac{4}{3} \pi R^{3} \rho}{R}} VeR \Rightarrow V_{e} \propto R VV=4RR\therefore \frac{V'}{V}=\frac{4 R}{R} V=4V \Rightarrow V^{'}=4 V