Assuming the earth to be a sphere of uniform density, the acceleration due to gravity inside the earth at a distance of $r$ from the centre is proportional to

Given below are two statements :

Statement$-I:$ Acceleration due to gravity is different at different places on the surface of earth.

Statement$-II:$ Acceleration due to gravity increases as we go down below the earth's surface.

In the light of the above statements, choose the correct answer from the options given below

If the Earth has no rotational motion, the weight of a person on the equator is $W$. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $\frac{3}{4}\,W$ . Radius of the Earth is $6400\, km$ and $g = 10\, m/s^2$

A body weight $ W $ newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to earth’s rotation.

A body weight $W$, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be