A cylindrical vessel containing a liquid is rotated about its axi… - Vidyadip

MCQ

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

✓
$\frac{25 \omega^{2}}{2 g}$
B
$\frac{2 \omega^{2}}{5 g}$
C
$\frac{5 \omega^{2}}{2 g}$
D
$\frac{2 \omega^{2}}{25 g}$

✓

Answer

Correct option: A.

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

a
Applying pressure equation from $A$ to $B$

$P_{0}+\rho \cdot \frac{R \omega^{2}}{2} \cdot R-\rho g h=P_{0}$

$\frac{\rho R ^{2} \omega^{2}}{2}=\rho gh$

$h =\frac{ R ^{2} \omega^{2}}{2 g }=(5)^{2} \frac{\omega^{2}}{2 g }=\frac{25}{2} \frac{\omega^{2}}{ g }$

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