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  • A metal cylinder of length  is subjected to a uniform compressive force <img alt="F" src="https://entrancecorner.onc

A metal cylinder of length L is subjected to a uniform compressive force F as shown in the figure.

The material of the cylinder has young's modulus Y and Poisson's ratio \sigma. The change in volume of th cylinder is:.
 

Option: 1

\frac{\mu F L}{Y}


Option: 2

\frac{(1-\sigma) F L}{Y}


Option: 3

\frac{(1+2 \sigma) F L}{Y}


Option: 4

\frac{(1-2 \sigma) FL}{Y}


Answers (1)

best_answer

 Using

 \frac{\Delta V}{V}=\frac{\Delta L}{L}(1-2 \sigma)
Here

\Delta L=\frac{F L}{A Y}

\begin{aligned} \therefore \quad \frac{\Delta V}{V} & =\frac{F}{A Y}(1-2 \sigma) \text { and } \Delta V=\frac{F}{A Y}(1-2\sigma) A L \\ \frac{\Delta V}{V} & =(1-2 \sigma) \frac{F L}{Y} \end{aligned}

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