A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is `sigma`. The angle of contact between water and the wall of the capillary tube is `theta`. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Options

A. For a given material of the capillary tube, h decreases with increase in r
B. For a given material of the capillary tube, h is independent of ` sigma `
C. If this experiment is performed in a lift going up with a constant acceleration, then h decreases
D. h is proportional to contact angle ` theta `

Answer

A, C

Explanation

` h = ( 2 sigma cos theta )/( r rho g ) `
` therefore ` h prop (1)/( r ) . ` If a lift is going up with a constant acceleration (a), then ` g_(eff) = g + a`. Since ` h prop (1)/(g_(eff)) `, so h decreases.