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?

This is a short answer type question as classified in NCERT Exemplar

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

Consider an elementary particle of the fluid of mass dm.

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

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

component of weight= component of pseudo force dmg sin $\theta$  =dma cos $\theta$   (we have assumed that the surface is inclined at an angle q) where, dma is pseudo force

g sin $\theta$ =acos $\theta$

a=g tan $\theta$

tan $\theta$ = a/g = slope

<p><span data-teams="true">This is a short answer type question as classified in NCERT Exemplar</span></p><p>Consider the diagram where a tanker is accelerating with acceleration a.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745474342phpqbzwdZ_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745474342phpqbzwdZ.jpeg" alt="" width="228" height="166"></picture></div></div><p>Consider an elementary particle of the fluid of mass dm.</p><p>The acting forces on the particle with respect to the tanker are shown above.</p><p>Now, balancing forces (as the particle is in equilibrium) along the inclined direction</p><p>component of weight= component of pseudo force dmg sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>&nbsp;=dma cos<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>&nbsp; (we have assumed that the surface is inclined at an angle q) where, dma is pseudo force</p><p>g sin<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>=acos<span contenteditable="false"> <math> <mi>θ</mi> </math> </span></p><p>a=g tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span></p><p>tan<span contenteditable="false"> <math> <mi>θ</mi> </math> </span>= a/g = slope</p>

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