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)/(brhog)cos(theta-alpha)`
B. `(2S)/(brhog)cos(theta+alpha)`
C. `(2S)/(brhog)cos(theta-alpha//2)`
D. `(2S)/(brhog)cos(theta+alpha)`

Answer

D

Explanation

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