A planet has twice the density of earth but the acceleration due to gravity on the surface is same as on the surface of earth. Its radius in terms of the radius R of earth is :

Options

A. `(R )/(64)`
B. `(R )/(8)`
C. `(R )/(4)`
D. `(R )/(2)`

Answer

D

Explanation

`g=(GM)/(R^(2))=(G)/(R^(2))xx(4)/(3)pi R^(2) rho =(4)/(3)pi R rho G`
`rArr R rho=(3g)/(4pi G)`
`rArr R rho=` Constant.
So if density is doubled, the radius is halved.
Hence correct choice choice is (d).