Question

9.
The length of a wire is increased by 0.3%. Find the
percentage increase in its volume, if Poisson's
ratio of wire material is 0.5.
14.​

Answer 1

Answer:

I think answer would be

the wire is increased by o.3%

0.(5.15).(14.2)

Answer 2

Answer:

The  percentage increase in its volume is 0.6 %.

Explanation:

Given that,

The length of a wire is increased by 0.3%.

Poisson's ratio = 0.5

Let the volume of the wire is V and change in volume is dV.

We need to calculate the change in volume

Using formula of volume

$\dfrac{dV}{V}=(1+2\sigma)\dfrac{dl}{l}$

Put the value into the formula

$\dfrac{dV}{V}=(1+2\times0.5)\times0.003$

$\dfrac{dV}{V}=0.006$

We need to calculate the percentage increase in its volume

$\dfrac{dV}{V}\times100=0.6\%$

Hence, The  percentage increase in its volume is 0.6 %.