Question

The density of core of a planet is P and that of outer shell The radius of core is R and that of planet is same as at the surfacce of core.The ratio.

Answer 1

Suppose, the 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 $\frac{Gm}{R^2}$.

And,on the surface of the shell it will be $\frac{G(m+m^{\prime })}{{\left(2R\right)}^2}$.

$\frac{Gm}{R^2}$=$\frac{G(m+m^{\prime })}{{\left(2R\right)}^2}$.

$4m=m+m^{\prime }$

$m=3m$

Let $m=\frac{4}{3}\pi R^3{\rho }_1$

$3m=3\left(\frac{4}{3}\pi R^3{\rho }_1\right)$$=m^{\prime }=\frac{4}{3}\pi 7R^3{\rho }_2$

${\rho }_1=\frac{7}{3}{\rho }_2$

$\frac{{\rho }_1}{{\rho }_2}=\frac{7}{3}$