First slide

Motion of planets and satellites

Question

The escape velocity of a body on an imaginary planet which is thrice the radius of the earth and double the mass of the earth is $(v_{e}$ is the escape velocity of earth)

Easy

A

$\sqrt{2 / 3} v_{e}$
B

$\sqrt{3 / 2} v_{e}$
C

$\sqrt{2} / 3 v_{e}$
D

$2 / \sqrt{3} v_{e}$

Solution

$\frac{v_{p}}{v_{e}} = \sqrt{\frac{M_{p}}{M_{e}} \times \frac{R_{e}}{R_{p}}} = \sqrt{\frac{2 M_{e}}{M_{e}} \times \frac{R_{e}}{3 R_{e}}} = \sqrt{2 \times \frac{1}{3}} = \sqrt{\frac{2}{3}} ∴ v_{p} = \sqrt{\frac{2}{3}} v_{e}$

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