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:

Given below are two statements:
Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement $II:$ Acceleration due to earth's gravity is same at a height '$h$' and depth '$d$' from earth's surface,if $h = d$.
In the light of above statements,choose the most appropriate answer from the options given below:

Consider Earth to be a sphere of radius $R_e$ rotating about its own axis with angular speed $\omega$. If $g_{E}$ and $g_{P}$ are the accelerations due to gravity at the equator and the poles respectively,then $(g_{P}-g_{E})$ is given by $\left[\cos (0^{\circ})=\sin (\frac{\pi}{2})=1, \sin (0^{\circ})=\cos (\frac{\pi}{2})=0\right]$

Acceleration due to gravity at the surface of a planet is equal to that at the surface of the Earth,and its density is $1.5$ times that of the Earth. If the radius of the Earth is $R$,the radius of the planet is:

By approximately how many meters is the radius of the Earth at the equator greater than the radius of the Earth at the poles (in $,000 \ m$)?

Two planets $A$ and $B$ of radii $R$ and $1.5 R$ have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to $A$ is: