# The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled

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The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a m s–2, what will be the slope of the free surface?.

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If the tanker acclerates in the positive x direction, then the water will bulge at the back of the tanker. The free surface will be such that the tangential force on any fluid parcel is zero.

Consider a parcel at the surface, of unit volume. The forces on the fluid are

-rgŷ and -ra

The component of the weight along the surface is rg sin θ

The component of the acceleration force along the surface is

r a cos θ

rg sin θ = ra cosθ

Hence, tan θ =a/g