Question

A solid rod of length L cross-sectional area A and density ρ is suspended freely in a wide tank filled with a liquid of density ρ₀ to a height h = L/η (where η > 1). The lower end of the rod touches the base of the tank.

(i) Determine the angle of inclination of the rod with the horizontal in the equilibrium position.

(ii) Determine the normal reaction between the rod and the base of the tank.

Answer 1

In the figure shown, let us assume

L= length of the rod

l = immersed length of the rod

θ = angle of inclination of rod with the horizontal. 

(i) If the rod is in equilibrium, then the net torque about the point A is zero, i.e.

(ii) Using New ton’s second law