Properties of Matter 4 Question 5
7. A uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended, with its length vertical from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extensition $x _0$ of the spring when it is in equilibrium is
(a) $\frac{M g}{k}$
(b) $\frac{M g}{k}\left(1-\frac{L A \sigma}{M}\right)$
(c) $\frac{M g}{k}\left(1-\frac{L A \sigma}{2 M}\right)$
(d) $\frac{M g}{k}\left(1+\frac{L A \sigma}{M}\right)$
(2013 Main)
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Answer:
Correct Answer: 7. $(a, c)$
Solution:
- $\Delta p _1=\frac{4 T}{r _1}$ and $\Delta p _2=\frac{4 T}{r _2}$
$$ r _1<r _2 \Rightarrow \Delta p _1>\Delta p _2 $$
$\therefore$ Air will flow from 1 to 2 and volume of bubble at end 1 will decrease.
Therefore, correct option is (b).
