A planet has double the mass of the earth. Its average density is...

The formula for acceleration due to gravity is

$g = \dfrac{GM}{{R}^{2}}$

Let the density of earth and planet be $ρ$, and the radius of the planet be $R '$. Let $R$ be the radius of the earth and $g$ be the acceleration due to gravity of earth and $g '$ be the acceleration due to gravity of planet.

So, the masses are

$M = \dfrac{4}{3}\pi{R}^{3}ρ . . . ( i )$

$M ' = \dfrac{4}{3}\pi{\left(R '\right)}^{3}ρ . . . ( ii )$

So, $\dfrac{g '}{{g}^{}} = \dfrac{\dfrac{GM '}{R{'}^{2}}}{\dfrac{GM}{{R}^{2}}} = \dfrac{M '}{M}{\left(\dfrac{R}{R '}\right)}^{2} . . . ( iii )$

From equation (i) and (ii) we get $R ' = 2\dfrac{1}{3}R$

Substituting the value in equation (iii),

$\dfrac{g '}{g} = \left({2}^{1}\right)2\dfrac{- 2}{3} = 2\dfrac{1}{3}g$

Weight is given by $W ' = mg ' = 2\dfrac{1}{3}W$