Question

In a capillary tube of area of cross-section '\(a\)' water rises to height '\(h\)'. To what height will water rise in a capillary tube of area of cross-section \(4a\)?

• A. \(\frac{h}{4}\)
• B. \(\frac{h}{2}\)
• C. \(2h\)
• D. \(4h\)

Hint:

Rise is inversely proportional to the radius, \(h\propto\frac1r\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In a capillary of radius \(r\), \(h=\dfrac{2T\cos\theta}{r\rho g}\), so \(h\propto\dfrac1r\).

Step 2: Key Formula or Approach
Area \(a=\pi r^2\), so area \(4a\) means radius \(2r\).

Step 3: Detailed Explanation
The radius doubles, so the height halves:
\[ h'=\frac h2 \]

Final Answer:
The new height is \(h/2\), option (B). \[ \boxed{\dfrac h2\ \text{(B)}} \]