1. Tardigrade
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  3. Physics
  4. The density of core of a planet is ρ1 and that of the outer shell is ρ2. The radii of core and that of the planet are R and 2R respectively. Gravitational acceleration at the surface of planet is same as at a depth. The ratio between (ρ 1/ρ 2) is

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Q. The density of core of a planet is $\rho_1$ and that of the outer shell is $\rho_2$. The radii of core and that of the planet are $R$ and $2R$ respectively. Gravitational acceleration at the surface of planet is same as at a depth. The ratio between $\frac{\rho _{1}}{\rho _{2}}$ is

Gravitation

Solution:

$\frac{Gm_{1}}{R^{2}} = \frac{G\left(m_{1}+m_{2}\right)}{\left(2R\right)^{2}}$
$4m_{1} = m_{1} + m_{2}$
$3m_{1} = m_{2}$
$3\left(\frac{4}{3}\pi R^{3}\rho_{1}\right)$
$ = \frac{4}{3}\pi\left[8R^{3}-R^{3}\right]\rho_{2}$
$3\rho_{1} = 7\rho_{2}$
$\frac{\rho _{1}}{\rho _{2}} = \frac{7}{3} = 2.3$