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Figure Shows a Capillary Tube of Radius R Dipped into Water. If the Atmospheric Pressure Is P0, the Pressure at Point A Is - Physics

MCQ

Figure shows a capillary tube of radius r dipped into water. If the atmospheric pressure is P0, the pressure at point A is

Options

  • P0

  • \[P_0 + \frac{2S}{r}\]

  • \[P_0 - \frac{2S}{r}\]

  • \[P_0 - \frac{4S}{r}\]

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Solution

\[\text{ Here }: \]

\[\text{ Radius of the tube = r }\]

\[\text{ Net upward force due to surface tension  = S }\text{ cos }\theta \times 2\pi r\]

\[\text{ Upward pressure }= \frac{\text{ S } cos \theta \times 2\pi r}{\pi r^2} = \frac{2Scos\theta}{r}\]

\[\text{ Net downward pressure due to atmosphere }= P_o \]

\[ \Rightarrow \text{ Net pressure at A }= P_o - \frac{2Scos\theta}{r}\]

\[\text{ Since }\theta \text{ is small, } \]

\[\text{ cos }\theta \approx 1 . \]

\[ \Rightarrow \text{ Net pressure }= P_o - \frac{2S}{r}\]

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 14 Some Mechanical Properties of Matter
MCQ | Q 18 | Page 298
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