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Coefficient of Viscosity

In a U - tube...

Question

In a U - tube the radii of two columns are respectively $r_{1}$ and $r_{2}$ . When a liquid of density $ρ (θ = 0^{\circ})$ is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is

A

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

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B

h ρ g (r_{2} - r_{1})

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C

\frac{h ρ g (r_{2} - r_{1})}{2}

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D

\frac{h ρ g}{2 (r_{2} - r_{1})}

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Solution

The correct option is A $\frac{ρ g h r_{1} r_{2}}{2 (r_{2} - r_{1})}$
$ρ g h = 2 T (\frac{1}{r_{1}} - \frac{1}{r_{2}}) = 2 T (\frac{r_{2} - r_{1}}{r_{1} r_{2}}) ∴ T = \frac{ρ g h r_{1} r_{2}}{2 (r_{2} - r_{1})}$

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