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 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

$A)\frac{2{\omega }^2}{25g}$ 

$B)\frac{5{\omega }^2}{2g}$ 

$C)\frac{25{\omega }^2}{5g}$ 

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

Answer 1

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

Explaination::

Applying pressure equation from A to B

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

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

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

 

 

Video Explaination From Kota doubt corner 

{this video does not belong to Brainiak Education Media , for removal request use feedback form }