In order to make the effective acceleration due to gravity equal to zero at the equator,the angular velocity of rotation of the earth about its axis should be $(g = 10\,m/s^2$ and radius of earth is $6400\,km)$.

If both the mass and the radius of the earth decrease by $1\%$,the value of the acceleration due to gravity will

If the mass of the Earth decreases by $25 \%$ and its radius increases by $50 \%$,then the acceleration due to gravity at its surface decreases by nearly ......... $\%$

Earth is assumed to be a sphere of radius $R$. If $g_{\phi}$ is the value of effective acceleration due to gravity at latitude $30^{\circ}$ and $g$ is the value at the equator,then the value of $|g - g_{\phi}|$ is ($\omega$ is the angular velocity of rotation of the Earth,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$).

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

What will be the acceleration due to gravity at a height $h$ above the Earth's surface,where $R$ is the radius of the Earth and $g$ is the acceleration due to gravity on the surface of the Earth?