The density of core of a planet is rho_1 and that of outer shell is rho_2. The radius of core is R and that of planet is 2R. Gravitational field at outer surface of planet is same as at the surface of core what is the ratio rho/rho_2. ?

(1)3/4
(2)5/3
(3)7/3
(4)3/5

1 Answer
Mar 15, 2018

3

Explanation:

Suppose, mass of the core of the planet is m and that of the outer shell is m'

So,field on the surface of core is (Gm)/R^2

And,on the surface of the shell it will be (G(m+m'))/(2R)^2

Given,both are equal,

so, (Gm)/R^2=(G(m+m'))/(2R)^2

or, 4m =m+m'

or, m'=3m

Now,m=4/3 pi R^3 rho_1 (mass=volume * density)

and, m'= 4/3 pi ((2R)^3 -R^3) rho_2=4/3 pi 7R^3 rho_2

Hence,3m=3(4/3 pi R^3 rho_1)=m'=4/3 pi 7R^3 rho_2

So, rho_1 =7/3 rho_2

or, (rho_1)/(rho_2)=7/3