When one moves from a point $16 \text{ km}$ below the earth's surface to a point $16 \text{ km}$ above the earth's surface, the change in $g$ is approximately $\alpha \%$. The value of $\alpha$ is . . . . . . . (Take radius of the earth $R = 6400 \text{ km}$.)

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

Assuming Earth to be a sphere of uniform density,what is the value of gravitational acceleration in a mine $100 \, km$ below the Earth's surface? (Given $R = 6400 \, km$,$g = 9.8 \, m/s^2$)

$A$ hole is drilled through the Earth along a diameter and a stone is dropped into it. When the stone reaches the center of the Earth,which of the following quantities remains constant?

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to the Earth's rotation.

The acceleration due to gravity is $g$ at a point distant $r$ from the centre of the Earth of radius $R$. If $r < R$,then: