Question

A U-tube of constant cross-section A contains liquid of density ρ. Initially, the liquids in the two arms are held with a level difference h. After being released, the levels equalize after some time. The work done by gravity forces on the liquid in the process is (W = ρAgh)

(a) zero 

(b) Wh 

(c) Wh/2 

(d) Wh/4

Answer 1

Correct Answer is: (d) Wh/4

The liquid levels will equalize at Q and R. This is equivalent to the section PQ moving down to the position RS.

Mass of section PQ = ρAh/ 2.

The centre of mass of this section moves down through a distance h/2.

Loss in potential energy

= (1/2 ρAh) g. (h/2) = 1/2 (ρAgh) h = 1/4 Wh

= work done by gravity forces on the liquid.