Calculate the difference in the value of $g$ at the equator and at the poles due to the rotation of the Earth.

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: If we move from poles to equator,the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason $R$: At equator,the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements,choose the correct answer from the options given below.

Suppose a vertical tunnel is dug along the diameter of the Earth,which is assumed to be a sphere of uniform mass having density $\rho$. If a body of mass $m$ is dropped into this tunnel,its acceleration at a distance $y$ from the center is given by

If acceleration due to gravity at distance $d < R$ from the centre of the Earth is $\beta$,then its value at distance $d$ above the surface of the Earth will be [where $R$ is the radius of the Earth].

If the radius of the Earth were to shrink by half while its density remains constant,what would be the weight of an object on the surface of the Earth?

The ratio of gravitational acceleration at height $3R$ to that at height $4R$ from the surface of the earth is (where $R$ is the radius of the earth):