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NEET PHYSICSMechanical Properties of FluidMedium

Question

A capillary tube of radius rr is immersed in water and water rises in it to a height hh. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r2r is immersed in water. The mass of water that will rise in this tube is:

A

5.0 g

B

10.0 g

C

20.0 g

D

2.5 g

Step-by-Step Solution

According to the sources, the height hh to which a liquid rises in a capillary tube of radius aa is given by the formula h=2Scosθρgah = \frac{2S \cos \theta}{\rho g a} . The mass (mm) of the liquid column is the product of its density (ρ\rho) and volume (VV). Assuming the liquid column is a cylinder of height hh, the volume is V=πa2hV = \pi a^2 h. Substituting the expression for hh into the mass formula: m=ρ×πa2×(2Scosθρga)m = \rho \times \pi a^2 \times \left( \frac{2S \cos \theta}{\rho g a} \right). Simplifying this gives m=2πaScosθgm = \frac{2 \pi a S \cos \theta}{g}. This derivation shows that the mass of the liquid in the capillary is directly proportional to the radius of the tube (mam \propto a) . Given that the first tube has radius rr and contains 5 g of water, a second tube with radius 2r2r (double the radius) will contain double the mass of water. Therefore, m2=2×5m_2 = 2 \times 5 g =10.0= 10.0 g.

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 Fluidcapillaryradiusimmersedheightcapillary

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