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Consider a capillary tube in which water has risen. The contact angle is θ. The radius of the capillary tube is ‘r’. The surface tension is ‘S’. And the density of water is ‘ρ’. What is the expression for the height of water risen in the tube? Assume the radius of meniscus to be ‘R’. Let the height of water risen in the tube be ‘h’.

Consider a capillary tube in which water has risen. The contact angle is θ. The radius of the capillary tube is ‘r’. The surface tension is ‘S’. And the density of water is ‘ρ’. What is the expression for the height of water risen in the tube? Assume the radius of meniscus to be ‘R’. Let the height of water risen in the tube be ‘h’. Correct Answer 2S / Rρg

In the given diagram the surface tension force will be acting along the red tangent. Therefore, the force is 2πrcosθ*S. This will be balanced by the weight of water risen in the tube. ∴ πr2 hρg = 2πrcosθ*S ∴ h = 2Scosθ / rρg = 2S / Rρg. (∵cosθ = r/R)

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