Question

10. The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in
the cross-sectional area by 4%. The percentage increase in the length is
(1)1%
(2) 2%
(4) 4%
(3)2.5%​

Answer 1

Answer:

4%

Explanation:

suppose r is thr radius of the wire, now if the area decreases by 4% it means

we have,

$4\pi r_{1} ^{2}$=0.96 ×4$\pi r^{2}$

$r_{1}$=$\sqrt{0.96} r$=0.98r

so decrease in radius is 2% hence the increase in length will be

                             =$\frac{2}{0.5}$

                            =4%

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