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: Ratio:
$\dfrac{h'}{h}=\dfrac r{r'}$.

Step 2: Area ratio:
$\dfrac{A'}{A}=\dfrac13=\left(\dfrac{r'}r\right)^2$, so $\dfrac{r}{r'}=\sqrt3$.

Step 3: Result:
$h'=3\sqrt3$ cm. Option (A).

Final Answer:
Area one third means radius divided by sqrt 3. \[ \boxed{A} \]