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NEET PHYSICSMechanical Properties of FluidEasy

Question

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height of the water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: [take \rho _water = 1000 kg/m^3]

A

1200 kg/m^3

B

750 kg/m^3

C

1000 kg/m^3

D

1333 kg/m^3

Step-by-Step Solution

  1. Principle: According to Pascal's Law and the principles of hydrostatics, the pressure at the same horizontal level in a continuous liquid at rest is the same . In a U-tube, the pressure exerted by the liquid columns at the level of the interface must be equal.
  2. Formula: The pressure exerted by a liquid column is given by P=ρghP = \rho g h, where ρ\rho is density, gg is acceleration due to gravity, and hh is the height of the column .
  3. Calculation: Equating the pressure exerted by the water column to that of the oil column: ρwaterghwater=ρoilghoil\rho_{water} g h_{water} = \rho_{oil} g h_{oil} 1000×g×15=ρoil×g×201000 \times g \times 15 = \rho_{oil} \times g \times 20 Canceling gg from both sides: 15000=20ρoil15000 = 20 \rho_{oil} ρoil=1500020=750 kg/m3\rho_{oil} = \frac{15000}{20} = 750 \text{ kg/m}^3

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Mechanical Properties of Fluid. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMechanical Properties of Fluidfigurerespectivelyheightcolumnsrespectively

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