Question

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

0.01
0.02
0.025
0.04

Answer 1

Note: I am writing sigma as ⊂.

Given Poisson's ratio (⊂) = 0.5.

Here, density is constant and hence change in volume is 0.

Given that there is a decrease in cross-sectional area by 4%

So, (dA/A) = 4.

We know that dA/A = 2 * (dr/r).

= > 4 = 2 * (dr/r)

= > 2 = (dr/r).

Hence,

= > dl/l

= > (dr/r)/⊂

= > 2/0.5

= > 4.

Therefore, the % increase in length = 4% (or) 0.04.

Hope this helps!

Answer 2

See above.......... attachment