Properties Of Matter Ques 24
- 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
(2013 Main)
(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) $\frac{M g}{k}\left(1+\frac{L A \sigma}{M}\right)$
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Answer:
Correct Answer: 24.( c )
Solution:
Here, $k x_0$ is restoring force of spring and $F_B$ is buoyancy force.
$ \begin{aligned} k x_0+\sigma \frac{L}{2} A g & =M g \\ x_0 & =\frac{M g-\frac{\sigma L A g}{2}}{k}=\frac{M g}{k}\left(1-\frac{\sigma L A}{2 M}\right) \end{aligned} $
BETA
