If the angular speed of the earth is doubled,the value of acceleration due to gravity $(g)$ at the north pole:

Consider a particle of mass $m$ suspended by a string at the equator. Let $R$ and $M$ denote the radius and mass of the Earth. If $\omega$ is the angular velocity of rotation of the Earth about its own axis,then the tension on the string will be $(\cos 0^{\circ}=1)$

If the radius of the Earth decreases without any change in its mass,will the value of $g$ on its surface increase or decrease?

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. $(R = 6.4 \times 10^6 \ m)$

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.

Explain the variations of acceleration due to gravity inside and outside the Earth and draw the graph.