Bulk Modulus & Compressibility question from JEE Main 2016 (10 Apr, Shift 1)

Answer: (d)

1. Only the radius changes (length $b$ fixed): $V = \pi r^2 b \Rightarrow \frac{\Delta V}{V} = \frac{2\Delta a}{a}$.
2. Pressure on the cork: $P = B\,\frac{\Delta V}{V} = \frac{2B\Delta a}{a}$
3. Normal force on the curved surface: $N = P\times2\pi a b = 4\pi B b\,\Delta a$
4. Force needed = friction $= \mu N = (4\pi\mu B b)\,\Delta a$
5. So the answer is (d).