A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 c m and its rotational s

Question

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 c m and its rotational speed is 2 rotations per second, then the difference in the heights between the center and the sides, in c m , will be:

TestHub · Accepted Answer

When cylinder is rotated, water will rise at the edge and will dip at the centre. The difference in pressure at $A$ and $O$ is $P_{A} - P_{0} = ρ g h .$ Due to height difference.

pressure difference $P_{1} - P_{0} = ρ \cdot a_{c m} R$ Due to rotation.

$= ρ \cdot (ω^{2} . \frac{R}{2}) R$

$∴ ρ g h = ρ \frac{ω^{2} R^{2}}{2} \Rightarrow h = \frac{ω^{2} \cdot R^{2}}{2 g} = {(2 π \times 2)}^{2} \times \frac{{(0.05)}^{2}}{2 \times 10}$

$= 0.02 m$

$= 2 c m$

Physics - Rotation Question with Solution | TestHub

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