First slide

Gravitaional potential energy

Question

The escape velocity on the surface of the earth is 11.2 km/s. If mass and radius of a planet is 4 and 2 times respectively than that of earth, what is the escape velocity from the planet ?

Easy

A

11.2 km/sec
B

1.112 km/sec
C

15.8 km/sec
D

22.4 km/sec

Solution

Escape velocity
$\begin{array}{l} = \sqrt{(2 g / R)} = \sqrt{2 (GM / R)} \\ = \sqrt{\frac{2 \times G \times 4 M}{2 R}} = \sqrt{2} \sqrt{(\frac{2 GM}{R})} \\ = \sqrt{2} \times 11 \cdot 2 = 15 \cdot 8 km / \sec \end{array}$

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