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…

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 &#160; 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:

Aicharya · 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

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical…

Solution