Question

Water rises to a height of $16.3\text{cm}$ in a capillary of height $18\text{cm}$ above the water level. If the tube is cut at a height of $12\text{cm}$,

• A. water will come out as a fountain from the capillary tube.
• B. water will stay at a height of $12\text{cm}$ in the capillary tube but radius of curvature at the top will increase.
• C. water will stay at a height of $12\text{cm}$ in capillary tube but radius of curvature at the top will decrease.
• D. water will flow down the side of the capillary tube.

Answer 1

The correct option is B water will stay at a height of $12\text{cm}$ in the capillary tube but radius of curvature at the top will increase.

It is force exerted by the tube that pulls the fluid up.
Here, the maximum height upto which the fluid can rise is $16.3\text{cm}$. If the height of the tube is only $12\text{cm}$, water will be able to rise upto $12\text{cm}$ because there is no space beyond $12\text{cm}$. No tube means no adhesive force and hence no pulling of fluid. So, water will stay at $12\text{cm}$.

We know, $h=\frac{2T}{\rho gR}$ where $R$ is the radius of curvature.
So, $R\propto \frac{1}{h}$ and since $h$ has decreased, $R$ increases.

Hence, option (b) is correct.