The distance through which one has to dig the earth from its surface so as to reach the point where the acceleration due to gravity is reduced by $40 \%$ of that at the surface of the earth,is (radius of earth is $6400 \ km$) (in $km$)

If the earth were to cease rotating about its own axis,the increase in the value of $g$ in the $C.G.S.$ system at a place of latitude of $45^{\circ}$ will be ........ $cm/sec^{2}$.

The weight of $1 \, kg$ becomes $1/6$ on the moon. If the radius of the moon is $1.768 \times 10^6 \, m$,then the mass of the moon will be:

The weights of an object are measured in a coal mine of depth $h_1$,then at sea level of height $h_2=0$,and lastly at the top of a mountain of height $h_3$ as $W_1, W_2$,and $W_3$ respectively. Which one of the following relations is correct? [$h_1 \ll R, h_3 \ll R, R=$ radius of the earth]

$Assertion$ : $A$ tennis ball bounces higher on hills than in plains.
$Reason$ : Acceleration due to gravity on the hill is greater than that on the surface of earth.

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