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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Mechanical Properties of Fluids

NEET 2016 · Physics · Mechanical Properties of Fluids

Three liquids of densities, ρ _ 1 , ρ _ 2 and ρ _ 3 (with, ρ _ 1 >...

Three liquids of densities, ρ1,ρ2{ρ}_{1}, {ρ}_{2} and ρ3{ρ}_{3} (with, ρ1>ρ2>ρ3){ρ}_{1} > {ρ}_{2} > {ρ}_{3} ), having the same value of surface tension,TT , rise to the same height in three identical capillaries. The angles of contact, θ1,θ2{\theta}_{1}, {\theta}_{2} and θ3{\theta}_{3} obey

Options

  1. Aπ2>θ1>θ2>θ3≥0\dfrac{\pi}{2} > {\theta}_{1} > {\theta}_{2} > {\theta}_{3} \ge 0
  2. B0≤θ1<θ2<θ3<π20 \le {\theta}_{1} < {\theta}_{2} < {\theta}_{3} < \dfrac{\pi}{2}
  3. Cπ2<θ1<θ2<θ3<π\dfrac{\pi}{2} < {\theta}_{1} < {\theta}_{2} < {\theta}_{3} < \pi
  4. Dπ>θ1>θ2>θ3>π2\pi > {\theta}_{1} > {\theta}_{2} > {\theta}_{3} > \dfrac{\pi}{2}

Correct answer

B. 0≤θ1<θ2<θ3<π20 \le {\theta}_{1} < {\theta}_{2} < {\theta}_{3} < \dfrac{\pi}{2}

Step-by-step solution

h=2Tcosθrρgh = \dfrac{2Tcos\theta}{rρg}.

⇒ρ∝cosθ⇒ ρ ∝ cos\theta(as T,hT, hand rr are constants).

Therefore, ρ↑⇒θ↓ρ ↑ ⇒ \theta ↓.

θ1<θ2<θ3{\theta}_{1} < {\theta}_{2} < {\theta}_{3}

The liquid is rising, so, 0≤θ1<θ2<θ3<π20 \le {\theta}_{1} < {\theta}_{2} < {\theta}_{3} < \dfrac{\pi}{2}.

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