Question

Water rises to a height \(3\) cm in a capillary tube. If cross-sectional area of capillary tube is reduced to \(1/3^{rd}\) of its initial area then water will rise to a height of

• A. \(3\sqrt{3}\) cm
• B. \(\sqrt{3}\) cm
• C. \(9\) cm
• D. \(3\) cm

Hint:

h is inversely proportional to r, not to area.

Answer 1

The Correct Option is A

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

Step 2: Radius from area:
Area \(A=\pi r^2\). If the area becomes \(\frac13\), then \(r^2\) becomes \(\frac13\) and \(r\to\dfrac r{\sqrt3}\).

Step 3: Height:
\[ h'=h\times\sqrt3=3\sqrt3\ \text{cm} \]

Step 4: Choose:
Option (A). Option (C), 9 cm, would be for the radius reduced to one third, not the area.

Final Answer:
The water rises to 3 sqrt 3 cm. \[ \boxed{3\sqrt3\ \text{cm}} \]