NEET2010PhysicsMechanical Properties of FluidsActual
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 radius of the vessel is r and angular velocity of rotation is , then the difference in the heights of the liquid at the centre of the vessel and the edge is
Options
- Ar 2 g
- Br^2 ^2 2 g
- C2 g r
- D^2 2 g r^2
Correct answer
B. r^2 ^2 2 g
Step-by-step solution
From Bernoulli's theorem, P_A+ 1 2 d v_A^2+d g h_A=P_B+ 1 2 d v_B^2+d g h_B Here, h_A=h_B aligned & P_A+ 1 2 d v_A^2=P_B+ 1 2 d v_B^2 & P_A-P_B= 1 2 d [v_B^2-v_A^2 ] & Now, v_A=0, v_B=r & and P_A-P_B=h d g aligned h d g= 1 2 d r^2 ^2 or h= r^2 ^2 2 g