When one end of a capillary tube is dipped in water, water rises to a height h. The upward force of 105 dyne due to surface tension is balanced by the force due to weight of water column. The inner ci

Question

When one end of a capillary tube is dipped in water, water rises to a height h. The upward force of 105 dyne due to surface tension is balanced by the force due to weight of water column. The inner circumference of the capillary is (surface tension of water = 7 × 1 0 − 2 N/m)

TestHub · Accepted Answer

The upward force due to surface tension in a capillary tube is given by $F = T \times L \times cos θ$ , where $T$ is the surface tension, $L$ is the inner circumference, and $θ$ is the angle of contact.

For water, the angle of contact $θ \approx 0^{\circ}$ , so $cos θ = 1$ .

Given:
Upward force $F = 105$ dyne $= 105 \times 1 0^{- 5}$ N
Surface tension $T = 7 \times 1 0^{- 2}$ N/m

Substituting the values into the formula:
$105 \times 1 0^{- 5} = (7 \times 1 0^{- 2}) \times L$

$L = \frac{105 \times 1 0 ^{- 5}}{7 \times 1 0 ^{- 2}}$

$L = 15 \times 1 0^{- 3}$ m

$L = 1.5 \times 1 0^{- 2}$ m $= 1.5$ cm

Answer: $1.5$ cm

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