A glass capillary tube is of the shape of a truncated cone with an apex angle `alpha` so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a high h, where the radius of its cross section is b. If the surface tension of water is S, its density if `rho`, and its contact angle with glass is `theta`, the value of h will be (g is the acceleration due to gravity)

Options

A. ` (2S )/(b rho g ) cos ( theta - alpha ) `
B. ` (2S ) /(b rho g ) cos ( theta+ alpha ) `
C. ` (2 S )/( b rho g ) cos ( theta - alpha//2 ) `
D. ` (2S )/( b rho g ) cos ( theta + alpha//2) `

Answer

D

Explanation

Let radius of curvature of meniscus
`b=rcos(theta+(alpha)/(2))` Excess pressure on concave side of meniscus = `(2S)/(r)`
`rArr(P_(0)+hrhog)-P_(0)=(2S)/(r)rArrhrhog=(2Scos(theta+(alpha)/(2)))/(b)"or"h=(2S)/(brhog)cos(theta+(alpha)/(2))`