First slide

Surface tension

Question

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75 x $10^{- 4}$ newton force due to the weight of the liquid. If the surface tension of water is $6 \times 10^{- 2}$ newton/metre the inner circumference of the capillary must be:

Moderate

A

$1.25 \times 10^{- 3} metre$
B

$0.50 \times 10^{- 2} metre$
C

$6.5 \times 10^{- 2} metre$
D

$12.5 \times 10^{- 2} metre$

Solution

Upward force due to surface tension,
$F_{u} = (2 πR) \times T$
where, 2 $π$ R --> Circumference of tube
$F_{u} = (2 πR) \times T,$
Because, surface tension is force per unit length.
$\Rightarrow 75 \times 10^{- 4} = (2 πR) \times 6 \times 10^{- 2}$
$∴ (2 πR) = \frac{75 \times 10^{- 4}}{6 \times 10^{- 2}} = 12.5 \times 10^{- 2} m$

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