Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A wire of volume is stretched to a longitudinal strain of . Find its change of volume if its Poisson's ratio is (a) , (b) , (c) .
Poisson's ratio: , between and . A stretched rod's volume changes by . The moduli are linked: and .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) .
Step 2. (b) : no change.
Step 3. (c) .
Answer: (a) . (b) . (c) .
Check. With the wire does not get thinner at all, so its volume grows by the full strain.
Watch out. The factor is : there are two sideways directions.
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