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BITSAT 2015
Exam
BITSAT
Year
2015
Subject
Physics
Chapter
Mechanical Properties of Fluids

BITSAT 2015 · Physics · Mechanical Properties of Fluids

A glass capillary tube of internal radius r=0.25mm is immersed in...

A glass capillary tube of internal radius r=0.25mm\mathrm{r}=0.25\mathrm{mm} is immersed in water. The top end of the tube projected by 2cm2 \mathrm{ cm} above the surface of the water. At what angle does the liquid meet the tube? Surface tension of water =0.7N/m=0.7 \mathrm{ N} / \mathrm{m}

Options

  1. Aθ=90∘\theta=90^{{}^{\circ}}
  2. Bθ=70∘\quad \theta=70^{{}^{\circ}}
  3. Cθ=45∘\theta=45^{{}^{\circ}}
  4. Dθ=35∘\theta=35^{{}^{\circ}}

Correct answer

B. θ=70∘\quad \theta=70^{{}^{\circ}}

Step-by-step solution

Water wets glass and so the angle of contact is zero. For full rise, neglecting the small mass in the meniscus 2πT=π\mathrmr2hρg⇒h=2Trρg[∵ water wets glass, θ=0∘] and  =2×0070.25×10−3×1000×9.8\begin{aligned}2 \pi \mathrm{T}&=\pi \mathrmr^{2} \mathrm{ h} \rho \mathrm{g} \Rightarrow \mathrm{h}=\frac{2 \mathrm{ T}}{\mathrm{r} \rho \mathrm{g}}\left[\because \text{ water wets glass, } \theta=0^{{}^{\circ}}\right] \\ \text{\text{ and } } =\frac{2 \times 007}{0.25 \times 10^{-3} \times 1000 \times 9.8} \end{aligned} As the tube is only 2cm2 \mathrm{ cm} above the water and so, water will rise by 2cm2 \mathrm{ cm} and meet the tube at an angle such that, 2πrT⁡cos⁡θ=πr2h′ρg⇒2Tcos⁡θ=h′rρg⇒cos⁡θ=h′rρg2T and  =2×10−2×0.25×10−3×1000×9.82×0.07\begin{aligned}2 \pi r & \operatorname{T} \cos \theta=\pi r^{2} h^{\prime} \rho g \\ \Rightarrow & 2 T \cos \theta= h^{\prime} r \rho g \\ \Rightarrow \cos \theta&=\frac{h^{\prime} r \rho g}{2 T}\\ \text{\text{ and } } =\frac{2 \times 10^{-2} \times 0.25 \times 10^{-3} \times 1000 \times 9.8}{2 \times 0.07} \end{aligned} The liquid will meet the tube at an angle, θ≅70∘\theta\cong 70^{{}^{\circ}}
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