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Tube of Insufficient Length

A liquid rise...

Question

A liquid rises to a height of $5 c m$ in a glass capillary of radius $0.02 c m$ . What will be the height of the same liquid in a glass capillary of radius $0.04 c m$ ?

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Solution

Given: $h_{1} = 5 c m$
$r_{1} = 0.02 c m$
$r_{2} = 0.04 c m$
$h_{2} = ?$
$T = \frac{r h ρ g}{2 cos θ}$
$r_{1} h_{1} = r_{2} h_{2}$
$5 \times 0.02 = 0.04 \times h_{2}$
$h_{2} = \frac{5 \times 0.02}{0.04} = 2.5 c m$

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