Q. 5

# The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the center of the earth? Think separately if the liquid is (a) at the equator (b) at a pole (c) somewhere else.

Here, we consider three different cases and discuss the direction of the net force on a liquid due to earth's gravity and rotation.

(a)At the Equator: Here, the force of gravity passes through center of the earth and the centrifugal force, which is the force due to rotation of the earth, is pointing vertically opposite to gravity but less in magnitude. Hence, normal to the free surface passes through the surface.

(b)At the Pole: Here, the centrifugal forces decrease to zero as the distance from the rotation axis is zero. Hence, only gravitational force acts on the liquid and the normal passes through the center of the earth.

(c) Somewhere else: In this situation, the centrifugal force will make some angle and hence the net force will not pass through the center.

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