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A long capillary glass tube of uniform diameter of $$1mm$$ is filled completely with water and then held vertically in air. It is now opened at both ends. Find the length of the water column remaining in the glass tube. Surface tension of water is $$0.075 N/m.$$ $$(g=10m/s^2$$ and density of water is $$10^3 kg/m^3)$$:


A
Zero
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B
1.5 cm
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C
3 cm
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D
6 cm
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Solution

The correct option is B 6 cm

Refer to the figure.
Pressure at a $$P_a= P_0-\dfrac{2T}{r}$$  .....(1)
Pressure at b $$P_b=P_0 + \dfrac{2T}{r}$$  .....(2)
Also, $$P_b -P_a = \rho gh$$
Substituting  $$P_a$$ and $$P_b$$ in 
$$ \therefore 2 \times  \dfrac{2T}{r} = \rho gh$$
$$ \Rightarrow h= \dfrac{4T}{r\rho g}= \dfrac{4 \times  0.075}{0.5 \times  10^{-3} \times  10^3 \times  10}=0.6 \times  10^{-1} \:m=6 \:cm$$

138540_75001_ans.JPG

Physics

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