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

Options

A. `W`
B. `2W`
C. `W//2`
D. `2^(1//3) W` at the planet

Answer

D

Explanation

`M_(p)=rho.4/3piR_(p)^(3), M_(e)=rho.4/3piR_(e)^(3)`
`(g_(p))/(g_(e))=(GM_(p)//R_(p)^(2))/(GM_(e).R_(e)^(2))=(M_(p))/(M_(e)).(R_(e)^(2))/(R_(p)^(2))=((M_(p))/(M_(e)))((M_(e))/(M_(p)))^(2//3)`
`=((M_(p))/(M_(e)))^(1//3)=(2)^(1//3)`
`(W_(p))/(W_(e))=(mg_(p))/(mg_(e))=(2)^(1//3)`
`W_(p)=(2)^(1//3)W_(e)=(2)^(1//3) W`