SATHEE: Properties of Matter 4 Question 5

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 $σ$ at equilibrium position. The extensition $x_{0}$ of the spring when it is in equilibrium is

(a) $\frac{M g}{k}$

(b) $\frac{M g}{k} (1 - \frac{L A σ}{M})$

(d) $\frac{M g}{k} (1 + \frac{L A σ}{M})$

(2013 Main)

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Answer:

Correct Answer: 7. $(a, c)$

Solution:

$Δ p_{1} = \frac{4 T}{r_{1}}$ and $Δ p_{2} = \frac{4 T}{r_{2}}$

$r_{1} < r_{2} \Rightarrow Δ p_{1} > Δ p_{2}$

$∴$ Air will flow from 1 to 2 and volume of bubble at end 1 will decrease.

Therefore, correct option is (b).

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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 σ at equilibrium position. The extensition x0 of the spring when it is in equilibrium is

Answer:

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