Acceleration due to gravity at a height $h$ is equal to that at a depth $d$ below the surface of the earth,if

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.

If $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth's surface,the mean density of the earth is

The ratio of the height $h$ above the surface of the Earth to the depth $d$ below the surface of the Earth,for which the gravitational accelerations are the same (assuming small heights),is:

Which of the following statements is true?

$A$ spherical part of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$ as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is