Question

Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio \(4: 3\). If their surface tensions are in the ratio \(6: 5\), the ratio of heights \(\left(\frac{h_1}{h_2}\right)\) of liquids in the two capillary tubes is (Their angle of contacts are same)

• A. \(\frac{10}{7}\)
• B. \(\frac{9}{10}\)
• C. \(\frac{10}{9}\)
• D. \(\frac{1}{2}\)

Hint:

Use h = 2T cos(theta)/(r rho g) with the same radius and contact angle.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Capillary rise: \(h=\frac{2T\cos\theta}{r\rho g}\). The tube radius, contact angle and g are the same.

Step 2: Ratio
\(h\propto\frac{T}{\rho}\), so \(\frac{h_1}{h_2}=\frac{T_1}{T_2}\times\frac{\rho_2}{\rho_1}\).

Step 3: Calculation
\(\frac{h_1}{h_2}=\frac{6}{5}\times\frac{3}{4}=\frac{18}{20}=\frac{9}{10}\).

Step 4: Compare the options
This is option (B).

Final Answer:
The ratio of heights is \(\frac{9}{10}\). \[ \boxed{\text{(B) }\dfrac{9}{10}} \]