Question

prove that loss in weight of a body is immersed only a partial in a liquid is equal to the upthrust and this loss is because of the difference in pressure exerted by liquid on the upper and lower surfaces of the summer as part of the body

Answer 1

Let
the depth at point a = h1
the depth at point b = h2
Now,
Pressure at point a and b is
Pa = rgh1 , Pb = rgh2
We know that
[Thrust = P . A ]
Thrust at point a = rgh1A
Thrust at point b = rgh2A
Net thrust = rgh2A - rgh1A
Net thrust = rgA(h2- h1)
[ But from figure h2- h1= L ]
There fore ,
Net thrust = rgAL 
Net thrust = rgV 
Net thrust = (rV)g 
Net thrust = mg
Net thrust = W
Net thrust = weight of liquid displaced.
This shows that upward thrust on the cylinder is equal to the weight of liquid displaced.