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NEET PHYSICSMechanical Properties of FluidEasy

Question

A barometer is constructed using a liquid (density = 760 kg/m³). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (the density of mercury = 13600 kg/m³)

A

1.36 m

B

13.6 m

C

136 m

D

0.76 m

Step-by-Step Solution

The pressure exerted by a fluid column is given by the formula P=ρghP = \rho gh, where ρ\rho is the density of the fluid, gg is the acceleration due to gravity, and hh is the height of the column , . In a barometer, the liquid column height represents the atmospheric pressure . Since both the mercury barometer and the alternative liquid barometer are measuring the same atmospheric pressure at the same location, their pressures must be equal: PHg=PliquidP_{\text{Hg}} = P_{\text{liquid}} . This gives the relation ρHgghHg=ρliquidghliquid\rho_{\text{Hg}} \cdot g \cdot h_{\text{Hg}} = \rho_{\text{liquid}} \cdot g \cdot h_{\text{liquid}}, which simplifies to ρHghHg=ρliquidhliquid\rho_{\text{Hg}} \cdot h_{\text{Hg}} = \rho_{\text{liquid}} \cdot h_{\text{liquid}}. Substituting the given values: 13600 kg/m30.76 m=760 kg/m3hliquid13600 \text{ kg/m}^3 \cdot 0.76 \text{ m} = 760 \text{ kg/m}^3 \cdot h_{\text{liquid}}. Solving for the height of the unknown liquid column: hliquid=(13600/760)0.76 m=180.76 m=13.6 mh_{\text{liquid}} = (13600 / 760) \cdot 0.76 \text{ m} = 18 \cdot 0.76 \text{ m} = 13.6 \text{ m}.

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 Fluidbarometerconstructedliquiddensityheight

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