JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Critical Thinking

  • question_answer
    A homogeneous solid cylinder of length L\[(L<H/2)\]. Cross-sectional area \[A/5\] is immersed such that it floats with its axis vertical at the liquid-liquid interface with length \[L/4\] in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure \[{{P}_{0}}\]. Then density D of solid is given by                                        [IIT-JEE 1995]

    A)             \[\frac{5}{4}d\]

    B)             \[\frac{4}{5}d\]

    C)             \[d\]

    D)             \[\frac{d}{5}\]

    Correct Answer: A

    Solution :

                       Weight of cylinder = upthrust due to both liquids                    \[V\times D\times g=\left( \frac{A}{5}\,\times \frac{3}{4}L \right)\times d\times g+\left( \frac{A}{5}\times \frac{L}{4} \right)\times 2d\times g\]             Þ\[\left( \frac{A}{5}\times L \right)\,\times D\times g=\frac{A\times L\times d\times g}{4}\]Þ\[\frac{D}{5}=\frac{d}{4}\] \[\therefore \ D=\frac{5}{4}d\]


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