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Q20 (NDA-I/2011) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

A liquid rises to a certain length in a capillary tube. The tube is inclined to an angle of 45°. The length of the liquid column will :

Result
Your answer:  ·  Correct: A
Explanation

According to Jurin's law, the vertical height (h) of a liquid column in a capillary tube is determined by the formula h = (2γ cosθ) / (ρgr), where γ is surface tension, θ is the contact angle, ρ is density, g is gravity, and r is the tube radius [t3][t8]. This vertical height depends only on the liquid's properties and the tube's radius, remaining constant regardless of the tube's orientation [t1]. When a capillary tube is inclined at an angle α to the vertical (or 45° in this case), the liquid must still reach the same vertical height (h) to maintain hydrostatic equilibrium. If 'L' is the length of the liquid column along the inclined tube, then h = L cosα. Consequently, L = h / cosα. Since cos(45°) is less than 1, the length (L) along the tube must increase to maintain the constant vertical height [t1].

Sources

  1. [1] https://en.wikipedia.org/wiki/Jurin%27s_law
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