Consider a planet in some solar system which has a mass double the mass of the earth and density equal to the average density of the earth. An object weighing W on the earth will weigh?

Since the density of planet is same as that of earth.
ρp=ρe
⇒Mp/(4/3πR³p) = Me/(4/3πR³e)
⇒Rp/Re = (Mp/Me)^(1/3)
The value of gravitational acceleration=
g=GM/R²
⇒Wp/We = (mg)p/(mg)e
⇒gp/ge = (Mp/Me)(R²e/R²p) = (Mp/Me)((Me/Mp)^(2/3)) = (Mp/Me)^(1/3) = 2^(1/3)
⇒Wp = 2^(1/3)W