Physics Circle home Student Login

Home›Chapters›Surface Tension PYQs›Angle of Contact & Capillarity›Question 52

MHT CET 2021 (23 Sep, Shift 2) · Angle of Contact & Capillarity

Angle of Contact & Capillarity question from MHT CET 2021 (23 Sep, Shift 2)

Q52MHT CET 2021 · 23 SEP · SHIFT 2Difficult

Angle of Contact & Capillarity

A glass rod of radius 'r1r_1 ' is inserted symmetrically into a vertical capillary tube of radius 'r2r_2' (r1<r2r_1 < r_2) such that their lower ends are at same level. The arrangement is dipped in water. The height to which water will rise into the tube will be (ρ=\rho = density of water, T = surface tension in water, g = acceleration due to gravity)

Show answer and solution

Answer: (a)

  1. Surface tension acts along both the tube wall (perimeter 2πr22\pi r_2) and the rod (perimeter 2πr12\pi r_1): F=2πT(r1+r2)F = 2\pi T(r_1 + r_2).
  2. Weight of water in the gap: W=π(r22−r12)hρgW = \pi(r_2^2 - r_1^2)h\rho g.
  3. F=W⇒h=2T(r1+r2)(r2−r1)(r2+r1)ρg=2T(r2−r1)ρgF = W \Rightarrow h = \dfrac{2T(r_1 + r_2)}{(r_2 - r_1)(r_2 + r_1)\rho g} = \dfrac{2T}{(r_2 - r_1)\rho g}.
  4. So the answer is (a) 2T(r2−r1)ρg\dfrac{2T}{(r_2 - r_1)\rho g}.
Report a mistake

More questions on Angle of Contact & Capillarity