Two narrow bores of diameter 5.0mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube.

[Take surface tension of water T = 7.3 × 10^-² Nm^-¹, angle of contact = 0, g = 10 ms^-² and density of water = 1.0 × 10³ kg m^-³]

Option 1 -

2.19mm

Option 2 -

4.97mm

Option 3 -

5.34mm

Option 4 -

3.62mm

2 Views | Posted 2 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

P_B – P_A = $ρ g h$

$\Rightarrow (P_{0} - \frac{2 T}{r^{2}}) - (P_{0} - \frac{2 T}{r_{1}}) = ρ g h$

$h = \frac{2 T (\frac{1}{r_{1}} - \frac{1}{r_{2}})}{ρ g}$

$= \frac{2 \times 7.3 \times 1 0^{- 2} \times (\frac{1}{2.5 \times 1 0^{- 3}} - \frac{1}{4 \times 1 0^{- 3}})}{1000 \times 10}$

$\begin{array}{l} = 2.19 \times 1 0^{- 3} m \\ = 2.19 m m \end{array}$

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