First slide

Motion of planets and satellites

Question

v_e and v_p denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then

Moderate

A

$v_{e} = v_{p}$
B

$v_{e} = v_{p} / 2$
C

$v_{e} = 2 v_{p}$
D

$v_{e} = v_{p} / 4$

Solution

$v_{e} = \sqrt{\frac{2 GM}{R}} = R \sqrt{\frac{8}{3} πGρ}$
If mean density is constant, then $v_{e} \propto R$
$\frac{v_{e}}{v_{p}} = \frac{R_{e}}{R_{p}} = \frac{1}{2} \Rightarrow v_{e} = \frac{v_{p}}{2}$

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