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

Answer

D

Explanation

buoyant force = force due to ST
`pi b^(2)h rho g=S 2 pi b cos (theta + alpha//2)`
or `h=(2S cos(theta + alpha//2))/(rho b g)`