Question

A cube floats in water with \(\left(\frac{1}{3}\right)^{th}\) part outside the surface of water. The same cube floats in another liquid with \(\left(\frac{3}{4}\right)^{th}\) part outside the liquid. If the density of liquid is \(\rho\), then the value of \(\rho\) in g/cc is (\(\rho _{w}\) = density of water = \(1\) g/cc)

• A. \(\frac{2}{3}\)
• B. \(\frac{4}{3}\)
• C. \(\frac{8}{3}\)
• D. \(\frac{10}{3}\)

Hint:

For a floating body, the density ratio equals the fraction of its volume immersed.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a floating body, \(\dfrac{\rho_{body}}{\rho_{liquid}}=\) fraction immersed.

Step 2: In water
\(\dfrac{1}{3}\) is outside, so \(\dfrac{2}{3}\) is immersed: \(\rho_{body}=\dfrac{2}{3}\times1=\dfrac{2}{3}\) g/cc.

Step 3: In the other liquid
\(\dfrac{3}{4}\) is outside, so \(\dfrac{1}{4}\) is immersed: \(\rho_{body}=\dfrac{\rho}{4}\).

Step 4: Calculation
\(\dfrac{\rho}{4}=\dfrac{2}{3}\), so \(\rho=\dfrac{8}{3}\) g/cc.

Final Answer:
The density of the liquid is 8/3 g/cc. \[ \boxed{\text{(C) }\dfrac{8}{3}} \]