Solved example of buoyancy force

Find specific gravity of oil in the given figure.

Solution: Forces acting on the Float are

1. its weight w acting downwards
2. the buoyant force F_B acting upward
3. the tension T in the rope acting downwards

Taking moments about A we get -

WX_G -F_BX_B =0     where

x_G and x_B are horizontal distances from A of the center of gravity and the center of buoyancy respectively.

where S_oil is the specific gravity of the oil.

(Buoyant force physics
Note: In the above equations length of float perpendicular to the plane of paper cancels out).

Now as mentioned earlier by moment balance.