Ncert Exercises & Solutions

Q. 17 The free surface of the 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?

Hint: Use the concept of equilibrium.

Step 1: Balance the forces for a particle at equilibrium.

Consider the diagram where a tanker is accelerating with an acceleration a.

Consider an elementary particle of the fluid of mass dm.

The forces acting on the particle with respect to the tanker are shown above.

Now, balancing the forces (as the particle is in equilibrium) along the inclined direction,

the component of weight = component of pseudo force

dmgsin

θ

= dmacos

θ

(we have assumed inclined at an angle

θ

)

where ma is the pseudo force

\Rightarrow g \sin θ = a \cos θ

\Rightarrow a = g \tan θ

\Rightarrow \tan θ = \frac{a}{g} = s l o p e

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