Fluid Mechanics Viscosity Question 73
Question: 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]
Options:
A) $ \frac{5}{4}d $
B) $ \frac{4}{5}d $
C) $ d $
D) $ \frac{d}{5} $
Show Answer
Answer:
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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