The depth at which acceleration due to gravity becomes $\frac{g}{n}$ is [ $R$ = radius of earth,$g$ = acceleration due to gravity,$n=$ integer].

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Maximum value of acceleration due to gravity $g$	$(a)$ At the center of the Earth
$(2)$ Minimum value of acceleration due to gravity $g$	$(b)$ At the poles
$(3)$ Zero value of acceleration due to gravity $g$	$(c)$ At the equator

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 weigh $\frac{3}{4} W$. The radius of the Earth is $6400 \ km$ and $g = 10 \ m/s^2$.

If the density of the Earth increases $4$ times and its radius becomes half of its present value,our weight will

Imagine a new planet having the same density as that of the earth, but it is two times bigger than the earth in size (radius). If the acceleration due to gravity on the surface of the new planet is $g'$ and that on the surface of the earth is $g$, then:

The period of oscillation of a simple pendulum of constant length at the Earth's surface is $T$. Its period inside a mine is