A planet has double the mass of the earth. It | vedclass

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(C) The mass of a planet is given by $M = ho 	imes \frac{4}{3} \pi R^3$,where $ho$ is the density and $R$ is the radius.Since the density $ho$

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$2^{1 / 3} W$

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(C) The mass of a planet is given by $M = ho 	imes \frac{4}{3} \pi R^3$,where $ho$ is the density and $R$ is the radius.Since the density $ho$ is constant,$M \propto R^3$,which implies $R \propto M^{1/3}$.The weight of an object is $W = mg$,where the acceleration due to gravity $g = \frac{GM}{R^2}$.Substituting $R \propto M^{1/3}$ into the expression for $g$,we get $g \propto \frac{M}{(M^{1/3})^2} = \frac{M}{M^{2/3}} = M^{1/3}$.Since the weight $W \propto g$,we have $W \propto M^{1/3}$.Given that the mass of the planet is double the mass of the earth $(M_p = 2M_e)$,the new weight $W'$ will be $W' = (2)^{1/3} W$.

$A$ 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 weigh on that planet:

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