Question

A wooden rod of a uniform cross section and of length 120cm is hinged at the bottom of the tank which is filled with water to a height of 40cm. In the equilibrium position, the rod makes an angle of with the vertical. The center of buoyancy is located on the rod at a distance (from the hinge) of:
(A) 20 cm
(B) 40 cm
(C) 60 cm
(D) 75 cm

Answer 1

The center of buoyancy is the point where all the mass of the fluid is supposed to be situated and at that point if all the displaced fluid is kept it will be perfectly balanced. This point is also called the center of mass. Since the rod remains in equilibrium, we can exploit this to came to a solution.

Complete step by step answer:
Given the length of the rod is 120 cm and it has a uniform cross section of area throughout.
Now out of this 120 cm, 80 cm of length is inside the water. Now, we know that centre of buoyancy plays the same role in a liquid as it is played by centre of mass in case of solids and since the composition of the rod is uniform throughout so center of buoyancy is at a distance of 40 cm from the hinge.

Note: sometimes we may get confused between centre of buoyancy and centre of gravity. Center of Gravity is the point in a body where the gravitational force acts on the body. This problem could also have been solved by using trigonometry to find out the immersed length but that would be time taking and lengthy too.