A large steel cylinder has inner radius ‘a’ as shown in the figure-(ii). There is a cork of radius $' a + Δ a' (Δ a < < a)$ and length ‘L’ shown in the figure (i). Now, cork is to be fitted to close the open mouth of cylinder. Consider poisson’s ratio of cork is almost zero and its bulk modulus is ‘B’. Choose the correct option(s).

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An uniform pressure on curved cylindrical surface of cork is developed which is equal to $\frac{2 B Δ a}{a}$

If $μ$ is the coefficient of friction between cork and container then the needed force to pull it out of the container is $2 π μ B L Δ a$ .

When stress is applied on a wire is increased beyond the yield point and is removed after some time then the wire can not return to its original position.

Steel is less elastic than cork

answer is B, D.

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Detailed Solution

$V = π a^{2} L d V = (2 π a L) d a Δ V = 2 π a L (Δ a) B = \frac{- Δ p}{(\frac{d V}{V})}, Δ p = \frac{2 B Δ a}{a} \Rightarrow F = μ (Δ) \times s u r f a c e a r e a F = μ \frac{2 B Δ a}{a} (2 π a L) = 4 π μ B L Δ a$