UPSEE Solved Model Paper 2

As the density of the liquid is constant, whole of the mass of liquid in the capillary is supposed to be concentrated at the h/2. So, the potential energy of the liquid in capillary is
U =

mgh

2

or,
The mass of the liquid in a column between x and x + dx is
dm = πr2ρdx
Therefore, the potential energy of the liquid in a column of height h is

h

∫

0

(πr2)xρgdx = πr2ρg‌

h

∫

0

xdx
= πr2ρg

h2

2

= (πr2hρ)gh∕2
= mgh/2