MHT CET202523 Apr 2025Evening ShiftPhysicsMechanical Properties of FluidsActual
A solid cylinder of length and cross-sectional area a 5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length / 4 in the denser liquid as shown in figure. The lower density liquid ( ) is open to atmosphere having pressure P₀ . The density d of solid cylinder is
Options
- A1 2
- B3 2
- C3 4
Correct answer
B. 3 2
Step-by-step solution
The density d of the solid cylinder is determined using the principle of flotation, where the weight of the object equals the total buoyant force exerted by the two fluids. With cross-sectional area A and length , the weight of the cylinder is d A g . The buoyant force from the denser liquid (density 3 ) acting on the immersed portion of length /4 is 3 A ( /4) g , and from the less dense liquid (density ) on the remaining 3 /4 is A (3 /4) g . Equating the weight to the sum of the buoyant forces gives: d A g = 3 A (