The weight of an object in the coal mine, sea level, at the top of the mountain are ${W_1},\;{W_2}$ and ${W_3}$ respectively, then

If a tunnel is cut at any orientation through earth, then a ball released from one end will reach the other end in time …….. $\min$ (neglect earth rotation)

Define acceleration due to gravity. Give the magnitude of $g$ on the surface of earth.

The value of acceleration due to gravity at Earth’s surface is $9.8\, m\,s^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9\, m\,s^{-2}$, is close to: (Radius of earth $= 6.4\times10^6\, m$)

In the reported figure of earth, the value of acceleration due to gravity is same at point $A$ and $C$ but it is smaller than that of its value at point $B$ (surface of the earth). The value of OA $: AB$ will be $x : y .$ The value of $x$ is $\ldots \ldots \ldots$