First slide

Motion of planets and satellites

Question

The escape velocity from the surface of earth is $V_{e}$ . The escape velocity from the surface of a planet whose mass and radius are 3 times those of the earth will be

Easy

A

$V_{e}$
B

$3 V_{e}$
C

$9 V_{e}$
D

$27 V_{e}$

Solution

$v_{e} = \sqrt{\frac{2 G M}{R}} ∴ v_{e} \propto \sqrt{\frac{M}{R}} \Rightarrow ∴ \frac{v_{2}}{v_{1}} = \sqrt{\frac{M_{2} R_{1}}{M_{1} R_{2}}} = \sqrt{\frac{4 M_{1} R_{1}}{M_{1} 4 R_{1}}} = 1 v_{1} = v_{2} = v_{e}$

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