A capillary tube of radius 0.1 mm is partly dipped in water. Surface tension is 70 dyn/cm, contact angle is 0°, and the tube is inclined at 30° with the vertical. Take g = 9.8 m/s². The length of the water column along the capillary is:
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Question

A capillary tube of radius 0.1 mm is partly dipped in water. Surface tension is 70 dyn/cm, contact angle is 0°, and the tube is inclined at 30° with the vertical. Take g = 9.8 m/s². The length of the water column along the capillary is:

Options

G1 Physics · Accepted Answer

First calculate the vertical capillary rise: h = 2Tcosθ/(ρgr). Use CGS-compatible values as in the source: T = 70 dyn/cm, θ = 0°, r = 0.1 mm = 0.01 cm, ρ = 1 g/cm³, g = 980 cm/s². Thus, h = 2(70)/(1×980×0.01) = 140/9.8 = 100/7 cm. The capillary is 30° from the vertical, so it is 60° from the horizontal. If ℓ is the length of water along the tube: h = ℓsin60°. Therefore, ℓ = h/sin60° = (100/7)(2/√3) ≈ 16.49 cm. Among the options, 82/5 = 16.4 cm is the matching value. Correct option: A.