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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

  1. A1 2
  2. B3 2
  3. 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 (

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