A) \[\left( 2\pi g\mu B\,\,b \right)\Delta a\]
B) \[\left( \pi \mu B\,\,b \right)\Delta a\]
C) \[\left( \pi \mu \,B\,\,b \right)a\]
D) \[\left( 4\pi \mu \,B\,\,b \right)\Delta a\]
Correct Answer: D
Solution :
\[\beta \frac{\Delta V}{V}=-\Delta P\] \[\Delta V\simeq -2\pi ab\Delta a\] \[{{V}_{f}}=\pi {{a}^{2}}b\] \[\frac{\Delta V}{V}=\frac{-2\pi ab\Delta a}{\pi {{a}^{2}}b}=\frac{-2\Delta a}{a}\] \[\Rightarrow \,\Delta P=\frac{2\beta \Delta a}{a}\] Normal force =\[=\frac{2\beta \Delta a}{a}2\pi ab\] \[=4\pi \beta \,\,b\,\Delta a\] friction \[=\mu N\] \[=4\pi \mu \beta \,b\Delta \,a\]
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