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NEET PHYSICSMechanical Properties of FluidEasy

Question

Water rises to a height hh in a capillary tube. If the length of the capillary tube above the surface of water is made less than hh, then:

A

water rises upto the tip of capillary tube and then starts overflowing like a fountain

B

water rises upto the top of capillary tube and stays there without overflowing

C

water rises upto a point a little below the top and stays there

D

water does not rise at all

Step-by-Step Solution

  1. Capillary Rise Formula: The height hh to which a liquid rises is given by h=2Tcosθrρgh = \frac{2T \cos \theta}{r \rho g}, where TT is surface tension, θ\theta is the angle of contact, rr is the tube radius, and ρ\rho is density .
  2. Insufficient Length: If the length of the tube LL is less than the calculated height hh (L<hL < h), the liquid will rise to the top of the tube.
  3. Adjustment of Meniscus: Upon reaching the top, the liquid does not overflow. Instead, the meniscus changes its shape. The radius of curvature of the meniscus (RR) increases (making the meniscus flatter), which effectively changes the contact angle θ\theta to a new value θ\theta'.
  4. New Equilibrium: The new condition for equilibrium becomes L=2TcosθrρgL = \frac{2T \cos \theta'}{r \rho g}. Since L<hL < h, it follows that cosθ<cosθ\cos \theta' < \cos \theta, meaning the contact angle increases. The liquid stays at the brim in equilibrium.

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 Fluidheightcapillarylengthcapillarysurface

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