Question

A horizontal thin tube of length 2L completely filled with a liquid of density `delta` rotates about a vertical axis passing through one of its end and along the diameter of its side face with an constant angular velocity `omega`. Two vertical thin long tubes are fitted with the horizontal tube to measure the pressure difference between points A and B which are at same horizontal level as shown. Neglect viscous forces and surfaces tension of liquid.

The difference in the heights (h) of the liquid column in the two vertical thin tubes is :
A. `(omega^(2)L^(2))/(2g)`
B. `(3 omega^(2)L^(2))/(2g)`
C. `(5 omega^(2)L^(2))/(2g)`
D. None of these

Answer 1

Correct Answer - B

`dm =deltaAdx`
`dPA =(delta Adx)a`
`(dP)/(dx)=delta omega^(3)x`
The difference in height
`h=y_(2)-y_(1)=(omega^(2)(2L)^(2))/(2g)-(omega^(2)L^(2))/(2g)=(3 omega^(2)L^(2))/(2g)`