KCET · Physics · Mechanical Properties of Fluids
Two solids \(P\) and \(Q\) float in water. It is observed that \(P\) floats with half of its volume immersed and \(Q\) floats with \(\frac{2}{3}\) rd of its volume is immersed. The ratio of densities of \(P\) and \(Q\) is
- A \(\frac{4}{3}\)
- B \(\frac{3}{4}\)
- C \(\frac{2}{3}\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{4}\)
Step-by-step Solution
Detailed explanation
The given situation can be shown as
\(\therefore \frac{V d P g}{V d Q g}=\frac{\frac{V}{2} \rho g}{\frac{2 V}{3} \rho g} \)
\( \Rightarrow \frac{d P}{d Q}=\frac{3 V \rho g}{4 V \rho g} \Rightarrow \frac{d P}{d Q}=\frac{3}{4}\)
\(\therefore \frac{V d P g}{V d Q g}=\frac{\frac{V}{2} \rho g}{\frac{2 V}{3} \rho g} \)
\( \Rightarrow \frac{d P}{d Q}=\frac{3 V \rho g}{4 V \rho g} \Rightarrow \frac{d P}{d Q}=\frac{3}{4}\)
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