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