If the density of the earth is doubled keeping the radius constant,find the new acceleration due to gravity (in $m/s^2$)? $(g = 9.8 \ m/s^2)$

$A$ point mass of $10 \,kg$ is placed at the centre of the Earth. The weight of the point mass is

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is

Acceleration due to gravity at the surface of a planet is equal to that at the surface of the Earth,and its density is $1.5$ times that of the Earth. If the radius of the Earth is $R$,the radius of the planet is:

The weight of a body at the centre of the earth is

Which of the following statements are true about the acceleration due to gravity of the Earth (where $r$ is the distance from the center of the Earth and $R$ is the radius of the Earth)?
$(a)$ $g$ decreases when moving away from the center, if $r > R$.
$(b)$ $g$ decreases when moving away from the center, if $r < R$.
$(c)$ $g$ is zero at the center of the Earth.
$(d)$ $g$ at the equator decreases, if the Earth stops rotating about its axis.