Consider a planet in some solar system that has a mass double the...

Consider a planet in some solar system that has a mass double the mass of earth and density equal to the average density of the earth. If the weight of an object on earth is

W

, the weight of the same object on that planet will be:

Options

A $2W$
B $W$
C $2\dfrac{1}{3}W$
D $\sqrt{2}W$

Correct answer

C. $2\dfrac{1}{3}W$

Step-by-step solution

Density is same

$M = \dfrac{4}{3}\pi{R}^{3}ρ, 2m = \dfrac{4}{3}\pi{R}^{' 3}ρ$

${R}^{'} = 2\dfrac{1}{3}R$

$W = \dfrac{GMm}{{R}^{2}}$

${W}_{2} = \dfrac{G2Mm}{{R}^{' 2}}$

${W}_{2} = 2\dfrac{1}{3}W$

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