The height at which the weight of a body becomes $\frac{1}{9}$ of its weight on the surface of the earth (radius of the earth is $R$) is:

The depth $d$ at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the surface is [$R =$ radius of the earth].

The value of $g$ at a particular point is $9.8\,m/s^2$. Suppose the Earth suddenly shrinks uniformly to half its present size without losing any mass. The value of $g$ at the same point (assuming that the distance of the point from the centre of the Earth does not shrink) will now be ......... $m/s^2$.

Given below are two statements:
Statement $I$: The law of gravitation holds good for any pair of bodies in the universe.
Statement $II$: The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements,choose the correct answer from the options given below.

If the earth stops rotating on its own axis,there will be no variation in the weight of our bodies at:

The angular velocity of the Earth at present is $\omega$. With what angular velocity should it rotate so that the weight of a body at the equator appears to be zero (in $\omega$)? (Express the answer as a multiple of $\omega$)