First slide

Gravitaional potential energy

Question

The escape velocity from the earth is 11 km/s. The escape velocity from a planet having twice the radius and same mean density as that of earth is :

Easy

A

5.5 km/s
B

11 km/s
C

22 km/s
D

none of the above

Solution

$v_{e} = \sqrt{\frac{2 GM}{R}} = \sqrt{\frac{2 G (\frac{4}{3} {πR}^{3}) ρ}{R}} \propto R$

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