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  • 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

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 the cylinder is

Option: 1

\frac{\mu F L}{Y}


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

Using, \frac{\Delta V}{V}=\frac{\Delta L}{L}(1-2 \sigma)
 Here,\Delta L=\frac{F L}{A Y}

\therefore \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}

Posted by

Ramraj Saini

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