Question 158: Properties of Matter

Question

A cylindrical vessel containing a liquid is
rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of
vessel is 5 cm and the angular speed of
rotation is $\omega $ rad s
–1
. The difference in the
height, h (in cm) of liquid at the centre of
vessel and at the side will be :
![](https://imagex.cdn.examgoal.net/jgy2xukeuzyo9n/a2a65770-17dc-477a-86df-34b72a9eb8fe/02e1c2b0-f265-11ea-8293-3b6cc591631c/file-jgy2xukeuzyo9o-184w.png)

Accepted Answer

Applying pressure equation from A to B
P
0
+ $\rho $.${{R{\omega ^2}} \over 2}$.R - $\rho $gh = P
0
$ \Rightarrow $ ${{\rho {R^2}{\omega ^2}} \over 2}$ = $\rho $gh
$ \Rightarrow $ h = ${{{R^2}{\omega ^2}} \over 2}$ = ${\left( 5 \right)^2}{{{\omega ^2}} \over {2g}}$ = ${{25} \over 2}{{{\omega ^2}} \over g}$
![](https://imagex.cdn.examgoal.net/1ki1l0lf3/fdd0b193-b660-4bde-a78f-a2695d5a11fd/b20b7ff0-3168-11eb-84ca-af07f68080f1/file-1ki1l0lf4-320w.png)

Answer

${{2{\omega ^2}} \over {25g}}$

Answer

${{5{\omega ^2}} \over {2g}}$

Answer

${{25{\omega ^2}} \over {2g}}$

Answer

${{2{\omega ^2}} \over {5g}}$

Properties of Matter

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