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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 ω rad s–1. The difference in the height, h (in cm) of liquid at the centre of vessel and at the side will be

\(A) \frac{2\omega^2}{25g}\) 

\(B) \frac{5\omega^2}{2g}\) 

\(C)\frac{25\omega^2}{5g}\) 

\(D) \frac{2\omega^2}{5g}\)

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Correct option is A) \(\frac{25\omega^2}{2g}\)  

Explaination::

Applying pressure equation from A to B

\(p_o+\rho.\frac{R\omega^2}{2}.R-\rho gh= p_o\) 

\(\rho.\frac{R^2\omega^2}{2}=\rho gh\) 

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

 

 

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