The mass of the moon is $7.34 \times 10^{22} \ kg$ and the radius of the moon is $1.74 \times 10^6 \ m$. The value of gravitational acceleration on the moon will be ....... $N/kg$.

What should be the angular speed of the Earth about its axis so that the acceleration due to gravity at the equator becomes zero?

At a height $R$ above the earth's surface,the gravitational acceleration is ($R$ = radius of earth,$g$ = acceleration due to gravity on earth's surface).

The depth $d$ at which the value of acceleration due to gravity becomes $\frac{1}{n}$ times the value at the earth's surface is $(R = \text{radius of the earth})$

How can we conclude that the Earth is not a perfect sphere based on the acceleration due to gravity?

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,$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$).