A uniform capillary tube of inner radius r is dipped vertically...

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

AFor a given material of the capillary tube, $h$ decreases with increase in $r$
BFor a given material of the capillary tube, $h$ is independent of $\sigma$
CIf this experiment is performed in a lift going up with a constant acceleration, then $h$ decreases
D $h$ is proportional to contact angle $\theta$

A. For a given material of the capillary tube, $h$ decreases with increase in $r$

\dfrac{2\sigma}{R} = ρgh \left[R \to Radiusofmeniscus\right]<br />

h =

\dfrac{2\sigma}{Rρg}

R =

\dfrac{r}{cos \theta} [r→radius of

capillary;\theta \to

contact angle]<br />

h =

\dfrac{2\sigma cos \theta}{rρg}<br />

( A )

For given material,

\theta = constant

<br />

h ∝

\dfrac{1}{r}<br />

( B )

h depends on

\sigma

<br />

( C )

If lift is going up with constant acceleration,<br />

{g}_{eff} = \left(g + a\right)

<br />

h = \dfrac{2\sigma cos \theta}{rρ\left(g + a\right)}

It means h decreases<br />

( D )

h is proportional to

cos \theta, Not\theta