WBJEE · Physics · Mechanical Properties of Fluids
A cylindrical block floats vertically in a liquid of density \(\rho_{1}\) kept in a container such that the fraction of volume of the cylinder inside the liquid is \(x_{1}\). Then some amount of another immiscible liquid of density \(\rho_{2}\left(\rho_{2} < \rho_{1}\right)\) is added to the liquid in the container so that the cylinder now floats just fully immersed in the liquids with \(x_{2}\), fraction of volume of the cylinder inside the liquid of density \(\rho_{1}\). The ratio \(\rho_{1} / \rho_{2}\) will be
- A \(\frac{1-x_{2}}{x_{1}-x_{2}}\)
- B \(\frac{1-x_{1}}{x_{1}+x_{2}}\)
- C \(\frac{x_{1}-x_{2}}{x_{1}+x_{2}}\)
- D \(\frac{x_{2}}{x_{1}}-1\)
Answer & Solution
Correct Answer
(A) \(\frac{1-x_{2}}{x_{1}-x_{2}}\)
Step-by-step Solution
Detailed explanation
The given situation is shown as As the Bouyant force in both the cases are same \(\therefore\) \[ \rho_{1} x_{1} g=\rho_{1} x_{2} g+\rho_{2}\left(1-x_{2}\right) g \] On solving \(\quad \frac{\rho_{1}}{\rho_{2}}=\frac{\left(1-x_{2}\right)}{\left(x_{1}-x_{2}\right)}\)
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