First slide

Gravitaional potential energy

Question

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

Easy

A

22 km/sec
B

11 km/sec
C

5.5 km/sec
D

15.5 km/sec

Solution

$v_{e} = \sqrt{\frac{2 GM}{R}} = \sqrt{\frac{8}{3} {πGρR}^{2}} as M = (\frac{4}{3} {πR}^{3}) ρ$

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