Question

Fig shows a cylinder of length L radius R density p/3 placed inside a tank. The tank contains a liquid of density ρ . The level of liquid in tank is H above the bottom of cylinder. The cylinder is in equilibrium, H is

(1) 4L/9

(2) 5L/3

(3) 5L/9

(4) 2L/3

Answer 1

(1) 4L/9

A₁ = Area of cross–section of cylinder πR²

A₂ = Area of cylinder in air = (R/2)² πR² /4

A₃ = Area of bottom of cylinder inside liquid = A₁ - A₂ = 3/4 πR²

Let P₀ be the atmospheric pressure. The forces acting on cylinder as shown in Fig. Obvisouly