Question
Show that a liquid at rest exerts a force perpendicular to the surface of the container at every point.
✓
Answer
Consider a liquid contained in a vessel in the equilibrium state of rest. As shown in Fig., suppose the liquid exerts a force F on the bottom surface in an inclined direction OA. The surface exerts an equal reaction R to water along OB.
The reaction R along OB has two rectangular components:
i. Tangential component, $OC = R \cos \theta$
ii. Normal component, $OD = R \sin \theta$
Since a liquid cannot resist any tangential force, the liquid near O should begin to flow along OC . But the liquid is at rest, the force along OC must be zero.
$
\therefore R \cos \theta=0
$
As $R \neq 0$, so $\cos \theta=0$ or $\theta=90^{\circ}$
Hence a liquid always exerts a force perpendicular to the surface of the container at every point.
The reaction R along OB has two rectangular components:
i. Tangential component, $OC = R \cos \theta$
ii. Normal component, $OD = R \sin \theta$
Since a liquid cannot resist any tangential force, the liquid near O should begin to flow along OC . But the liquid is at rest, the force along OC must be zero.
$
\therefore R \cos \theta=0
$
As $R \neq 0$, so $\cos \theta=0$ or $\theta=90^{\circ}$
Hence a liquid always exerts a force perpendicular to the surface of the container at every point.
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