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MHT CET 2024 (9 May, Shift 2) · Angle of Contact & Capillarity

Angle of Contact & Capillarity question from MHT CET 2024 (9 May, Shift 2)

Q38MHT CET 2024 · 9 MAY · SHIFT 2Medium

Angle of Contact & Capillarity

Three liquids of densities ρ1,ρ2\rho_1, \rho_2 and ρ3\rho_3 (with ρ1>ρ2>ρ3\rho_1 > \rho_2 > \rho_3) having same value of surface tension T, rise to the same height in three identical capillaries. Angle of contact θ1,θ2\theta_1, \theta_2 and θ3\theta_3 respectively obey

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Answer: (b)

  1. All three rise, so each θ<π2\theta < \frac{\pi}{2} (cos⁡θ>0\cos\theta > 0).
  2. Same hh, TT, rr: cos⁡θ∝ρ\cos\theta \propto \rho; ρ1>ρ2>ρ3⇒cos⁡θ1>cos⁡θ2>cos⁡θ3\rho_1 > \rho_2 > \rho_3 \Rightarrow \cos\theta_1 > \cos\theta_2 > \cos\theta_3.
  3. So 0≤θ1<θ2<θ3<π20 \le \theta_1 < \theta_2 < \theta_3 < \frac{\pi}{2}; the answer is (b).
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