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: Relate area to radius
$r\propto\sqrt a$, so $r'=2r$.

Step 2: Use $hr=$ constant
$h'r'=hr$ gives $h'=h/2$, option (B).

Final Answer:
Water rises to $h/2$, option (B). \[ \boxed{\dfrac h2} \]