A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weight on that planet :

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$2 W$

$2^{2 / 3} W$

$2^{1 / 3} W$

$W$

answer is B.

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Detailed Solution

$Let mass of earth = M & Density = ρ$

Acceleration due to gravity

$\begin{array}{l} = \frac{G M}{R^{2}} \\ = \frac{4 π}{3} ρ G R \end{array}$

Weight = W

On other planet of mass = 2M

$\begin{array}{l} ρ {(R^{1})}^{3} = 2 ρ R^{3}; R^{1} = 2^{1 / 3} R \\ g^{1} = \frac{4 π}{3} ρ G R (2^{1 / 3}) \\ W^{1} = 2^{1 / 3} W \end{array}$

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