A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base .If the redius of the vessel is r and angular velocity of rotation is omega, then the difference in the heights of the liquid at the centre of the vessel and the edge is .....

A liquid is kept in a cylindrical vessel which is being rotated about

1.	A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base .If the redius of the vessel is r and angular velocity of rotation is omega, then the difference in the heights of the liquid at the centre of the vessel and the edge is .....
Answer» `(romega)/(2g)` `(R^(2)omega^(2))/(2g)` `sqrt(2gromega)` `(omega^(2))/(2gr^(2))` Solution :ACCORDING to Bernoulli.s equation, `P_(A)+(1)/(2)rhov_(A)^(2)+rhogh_(A)` `=P_(B)+(1)/(2)rhov_(B)^(2)+rhogh_(B)` Here , `h_(A)=h_(B)` `thereforeP_(A)+(1)/(2)rhov_(A)^(2)` `=P_(B)+(1)/(2)rhov_(B)^(2)` `thereforeP_(A)-P_(B)=(1)/(2)rho[v_(B)^(2)-v_(A)^(2)]` Now ,`v_(A)=0,v_(B)-romegaandP_(A)-P_(B)=rhog` `thereforehrhog=(1)/(2)RHOR^(2)omega^(2)orh=(r^(2)omega^(2))/(2g)`