Question

Pure water rises through a height \(h\) in a capillary tube of internal radius r . Surface tension of water is T . The pressure difference between the water level in the container and the lowest point of the concave meniscus is

• A. \(\frac{\mathrm{r}}{\mathrm{T}}\)
• B. \(\frac{\mathrm{T}}{\mathrm{r}}\)
• C. \(\frac{2T}{r}\)
• D. \(\frac{\mathrm{r}}{2\text{ }\mathrm{T}}\)

Hint:

Just below a concave meniscus the pressure is less than atmospheric by the excess pressure of the curved surface.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The level in the container is at atmospheric pressure \( P_0 \). A concave meniscus makes the pressure on the liquid side lower than the outside pressure.

Step 2: Excess Pressure
For a hemispherical meniscus of radius \( r \) (zero contact angle), the pressure just below it is \( P_0-\dfrac{2T}{r} \).

Step 3: Difference
\( \Delta P=P_0-\left(P_0-\dfrac{2T}{r}\right)=\dfrac{2T}{r} \)

Step 4: Compare the options
This matches option (C).

Final Answer:
The pressure difference is 2T divided by r. \[ \boxed{\text{(C) }\dfrac{2T}{r}} \]