Properties of Matter 2 Question 6

6. A homogeneous solid cylinder of length $L$ and 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 figure. The lower density liquid is open to atmosphere having pressure $p _0$.

Then, density $D$ of solid is given by

(a) $\frac{5}{4} d$

(b) $\frac{4}{5} d$

(c) $4 d$

(d) $\frac{d}{5}$

$(1995,2 M)$

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Answer:

Correct Answer: 6. (c)

Solution:

Considering vertical equilibrium of cylinder

Weight of cylinder $=$ Upthrust due to upper liquid + upthrust due to lower liquid

$\therefore \quad(A / 5)(L) D g=(A / 5)(3 L / 4)(d) g$ $+(A / 5)(L / 4)(2 d)(g)$

$$ \begin{aligned} \therefore \quad D & =\left(\frac{3}{4}\right) d+\left(\frac{1}{4}\right)(2 d) \\ D & =\frac{5}{4} d \end{aligned} $$



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