Question

A cylinder is elongated by 2 % of its original length if the poisson's ratio of its material is 0.3 t,the percentage variation in volume is

Answer 1

Answer:

there is an decrement of 6.66% in volume.

Answer 2

Given that,

A cylinder is elongated by 2 % of its original length.

$\dfrac{\Delta L}{L}=0.02$

Poisson's ratio = 0.3

We need to calculate the change in volume

Using formula of poisson ratio

$\sigma=\dfrac{\dfrac{\Delta L}{L}}{\dfrac{\Delta V}{V}}$

$\sigma=\dfrac{\dfrac{\Delta L}{L}}{\dfrac{\Delta V}{V}}$

$\dfrac{\Delta V}{V}=\dfrac{\dfrac{\Delta L}{L}}{\sigma}$

Put the value into the formula

$\dfrac{\Delta V}{V}=\dfrac{0.02}{0.3}$  

$\dfrac{\Delta V}{V}\times100=\dfrac{0.02}{0.3}\times100$

$\dfrac{\Delta V}{V}\times100=6.67\%$

Hence, The percentage variation in volume is 6.67 %.