Correct Answer is: (c) be moving with a velocity of (h1-h2) √(g/2(h1+h2+h))
When the levels equalize,
the height of the liquid in each arm = h1+h2/2
We may then visualize that a length h1 - h1+ h2 / 2 = h1 - h2 / 2 of the liquid has been transferred from the left arm to the right arm. Then,
mass of this liquid = (h1 - h2 / 2) aρ,
where, A = area of tube, ρ = density of the liquid.
Distance through which it moves down = h1 - h2 /2.
∴ loss in gravitational potential energy = (h1 - h2 / 2) Aρ.
The mass of the entire liquid = (h1 + h2 + h) Aρ.
If this moves with a velocity v,
its kinetic energy = 1/2 (h1 + h2 + h) Aρv2
Equating energies, we get v.