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)

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:

$(a)$ Earth can be thought of as a sphere of radius $6400 \, km$. Any object (or a person) is performing circular motion around the axis of the Earth due to the Earth's rotation (period $1 \, \text{day}$). What is the acceleration of an object on the surface of the Earth (at the equator) towards its centre? What is it at latitude $\theta$? How do these accelerations compare with $g = 9.8 \, m/s^2$?
$(b)$ The Earth also moves in a circular orbit around the Sun once every year with an orbital radius of $1.5 \times 10^{11} \, m$. What is the acceleration of the Earth (or any object on the surface of the Earth) towards the centre of the Sun? How does this acceleration compare with $g = 9.8 \, m/s^2$?

If a tunnel is cut at any orientation through the Earth,a ball released from one end will reach the other end in time ........ $\text{min}$ (neglect Earth's rotation).

Two identical thin uniform rods of mass $M$ and length $L$ are placed in a line at a separation of $L$. Find the gravitational force acting between them.

Particles of mass $100 \, g$ each are placed at the vertices of an equilateral triangle of side $20 \, cm$. How much work must be done to increase the separation between them to infinity?