Assuming the density of the Earth is constant, which graph correctly represents the variation of acceleration due to gravity $(g)$ with the distance $(r)$ from the center of the Earth (radius of the Earth $= R$)?

Which of the following statements are true about the acceleration due to gravity,$g$?
$A$. $g$ is greater at the poles.
$B$. The value of $g$ decreases with height.
$C$. The value of $g$ is the same all over the Earth.
$D$. The value of $g$ is maximum at the center of the Earth.

What is the acceleration due to gravity at a distance of $2R$ from the surface of the Earth,where $R$ is the radius of the Earth?

The acceleration due to gravity at a height of $6400 \,km$ from the surface of the earth is $2.5 \,ms^{-2}$. The acceleration due to gravity at a height of $12800 \,km$ from the surface of the earth is (Radius of the earth $= 6400 \,km$) (in $\,ms^{-2}$)

Define acceleration due to gravity. Give the magnitude of $g$ on the surface of earth.

Find the angular speed of rotation of the Earth,so that the apparent $g$ at the equator becomes $(1/6)$th of its original value. $(R = 6.4 \times 10^6 \ m)$