NTA Abhyas JEE Main2020PhysicsMechanical Properties of FluidsPractice
The U - tube shown has a uniform cross-section. A liquid is filled in the two arms up to heights h 1 and h 2 , and then the liquid is allowed to move. Neglect viscosity and surface tension. When the levels equalize in the two arms, the liquid will
Options
- ABe at rest
- BBe moving with an acceleration of g h 1 - h 2 h 1 + h 2 + h
- CBe moving with a velocity of h 1 - h 2 g 2 h 1 + h 2 + h
- DExert a net force to the right on the tube.
Correct answer
C. Be moving with a velocity of h 1 - h 2 g 2 h 1 + h 2 + h
Step-by-step solution
When the levels equalize, the height of the liquid in each arm = h 1 + h 2 2 We may then visualize that a length h 1 - h 1 + h 2 2 = h 1 - h 2 2 of the liquid has been transferred from the left arm to the right arm. Then, the mass of this liquid = h 1 - h 2 2 A ρ where, A = area of tube, ρ = density of the liquid Distance through which it moves down = h 1 - h 2 2 ∴ Loss in the gravitational potential energy = h 1 - h 2 2 2 A ρg The mass of the entire liquid = h 1 + h 2 + h A ρ If this move