99 Percentile Qs Bank for JEE MainPhysicsMechanical Properties of Fluids
A closed tube filled with water is rotating uniformly in a horizontal plane about the axis O O ' as shown in the figure. The manometers A and B which are fixed on the tube at distances r 1 and r 2 , indicate pressures P 1 and P 2 respectively. The angular velocity ( ω ) of the tube is
Options
- Aω = 2 P 2 - P 1 ρ r 2 2 - r 1 2
- Bω = 2 P 2 + P 1 ρ r 2 2 - r 1 2
- Cω = 2 P 2 + P 1 ρ r 2 2 + r 1 2
- Dω = 2 P 2 - P 1 ρ r 2 2 + r 1 2
Correct answer
A. ω = 2 P 2 - P 1 ρ r 2 2 - r 1 2
Step-by-step solution
Consider the condition of equilibrium for the mass of water contained between cross section separated by x and x + d x from rotation axis. d p = ρ ω 2 x d x ; ∫ p 1 p 2 d p = ∫ r 1 r 2 ρ ω 2 x d x p 2 - p 1 = ρ ω 2 x 2 2 r 1 r 2 = ρ ω 2 r 2 2 - r 1 2 2 ω = 2 P 2 - P 1 ρ r 2 2 - r 1 2