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Q.

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

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a

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

b

$v_{e} = v_{p}$

c

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

d

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

answer is B.

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Detailed Solution

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$v_{e} = \sqrt{\frac{2 GM}{R}} = R \sqrt{\frac{8}{3} πGρ}$

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