What is the intensity of the gravitational field at the center of a spherical shell?

The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho(r) = \rho_{0} \left(1 - \frac{r^{2}}{R^{2}}\right)$. Then the gravitational field is maximum at:

If the distance between the centres of Earth and Moon is $D$ and the mass of Earth is $81$ times that of the Moon,at what distance from the centre of Earth will the gravitational field be zero?

$A$ ring has a mass $M$ and radius $R$. The distance of the point on its geometric axis from its centre at which the gravitational field is strongest is

The mass of the Earth is $81$ times the mass of the Moon and the distance between their centres is $R$. The distance from the centre of the Earth where the gravitational force will be zero is

Two concentric shells of masses $m_1$ and $m_2$ have radii $r_2$ and $r_1$ respectively (where $r_2 < r_1$). $A$ particle of mass $m$ is placed at positions $A, B,$ and $C$ as shown in the figure. The gravitational forces on the particle at these positions are: