Correct Option
When an oil tanker accelerates uniformly forward, the oil inside it experiences a pseudo force in the direction opposite to the acceleration. This pseudo force effectively pushes the fluid towards the rear end of the tanker. Consequently, the oil accumulates at the rear, causing the free surface to tilt. The depth of the oil becomes larger at the rear end and shallower at the front end, resulting in an inclined surface.
Incorrect Options:
- (a) remains horizontal: The free surface of a fluid remains horizontal only when the container is at rest or moving with constant velocity (zero acceleration). In the presence of uniform acceleration, the fluid surface will incline.
- (b) is inclined to the horizontal with smaller depth at the rear end: Due to the pseudo force acting opposite to the direction of acceleration, the fluid is pushed towards the rear. This causes the depth at the rear end to increase, not decrease.
- (d) assumes a parabolic curve: A parabolic free surface is observed when a fluid in a container is rotated about a vertical axis (rotational motion). In uniform linear acceleration, the free surface forms a plane inclined at a constant angle, not a parabolic curve.