MCQ
A glass capillary tube of internal radius $r=0.25\,mm$ is immersed in water. The top end of the tube projected by $2\,cm$ above the surface of the water. At $...........^{\circ}$ angle does the liquid meet the tube.Surface tension of water $=0.7\,N / m$.
  • $70$
  • B
    $90$
  • C
    $45$
  • D
    $35$

Answer

Correct option: A.
$70$
a
Water wets glass and so the angle of contact is zero.

Neglecting the small mass in the meniscus, for full rise,

$2 \pi r T=\pi r^2 h \rho g$

$\rho=\frac{2 T}{r \rho g}=\frac{2 \times 0.07}{0.25 \times 10^{-3} \times 1000 \times 9.8}=0.057 m =5.7 cm$

But there the tbe is only $2 cm$ above the water and so water will rise by $2 cm$ and meet the tube at an angle such that

$2 \pi r T \cos 0^{\circ}=\pi r^2 h^{\prime} \rho g$

$\Rightarrow 2 T \cos \theta=h^{\prime} r \rho g$

$\Rightarrow \cos \theta=\frac{h^{\prime} r \rho g}{2 T}$

$\therefore \cos \theta=\frac{2 \times 10^{-2} \times 0.25 \times 10^{-3} \times 1000 \times 9.8}{2 \times 0.07}$

$\Rightarrow \theta=70^{\circ}$

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