Question

An object of density \( \rho \) is floating in a liquid with 75% of its volume submerged. The density of the liquid is:

• A. \( \frac{4}{3}\rho \)
• B. \( \frac{3}{2}\rho \)
• C. \( \frac{8}{5}\rho \)
• D. \( 2\rho \)

Hint:

For floating bodies, the fraction of volume submerged equals the ratio of object’s density to the liquid’s density.

Answer 1

The Correct Option is A

Step 1: Use the principle of flotation.
A floating object displaces liquid whose weight equals its own: \[ \rho_{\text{object}} V g = \rho_{\text{liquid}} V_{\text{sub}} g. \] Step 2: Simplify the relation.
\[ \frac{\rho_{\text{object}}}{\rho_{\text{liquid}}} = \frac{V_{\text{sub}}}{V}. \] Given \( \frac{V_{\text{sub}}}{V} = 0.75 \), we get \[ \rho_{\text{liquid}} = \frac{\rho}{0.75} = \frac{4}{3}\rho. \]
Step 3: Final Answer.
Density of the liquid is \( \frac{4}{3}\rho. \)