The variation of acceleration due to gravity $g$ with distance $d$ from the centre of the earth is best represented by ($R =$ Earth's radius)

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

The acceleration due to gravity on the earth's surface at the poles is $g$ and the angular velocity of the earth about the axis passing through the poles is $\omega$. An object is weighed at the equator and at a height $h$ above the poles by using a spring balance. If the weights are found to be the same,then $h$ is: ($h << R$,where $R$ is the radius of the earth)

The weight of an object in a coal mine,at sea level,and at the top of a mountain are $W_1$,$W_2$,and $W_3$ respectively. Then:

What is the height from the surface of earth,where acceleration due to gravity will be $\frac{1}{4}$ of that of the earth (in $km$)? $(R_E = 6400 \ km)$

$A$ tunnel is dug through the centre of the earth. Show that a body of mass $m$ when dropped from rest from one end of the tunnel will execute simple harmonic motion.