Question

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.
1) 0.3%
2)0.9%
3)0.27%
4)0%

please give the whole solution not just the answer. ​

Answer 1

The volume of the wire is increased by 0.6%.

Explanation:

Given data:  

Length of the wire is increased by 0.3% therefore,  

dL/L = 0.003

Poisson’s ratio of wire material, σ = 0.5

To find: percentage increase in volume

Let the volume of the wire be “V” and the change in the volume “dV”.

The increase in volume is given by

dV/V = (1 + 2 σ) dL/L  

or, dV/V        

= (1 + 2 * 0.5) * 0.003  

= 2 * 0.003

= 0.006

Thus,  

∴ Percentage increase in the volume of the wire is  

= 0.006 * 100%  

= 0.6 %

Answer 2

$\huge\underbrace\mathfrak \red{ANSWER }$

The volume of the wire is increased by 0.6%.

Explanation:

Given data:  

Length of the wire is increased by 0.3% therefore,  

dL/L = 0.003

Poisson’s ratio of wire material, σ = 0.5

To find: percentage increase in volume

Let the volume of the wire be “V” and the change in the volume “dV”.

The increase in volume is given by

dV/V = (1 + 2 σ) dL/L  

or, dV/V        

= (1 + 2 * 0.5) * 0.003  

= 2 * 0.003

= 0.006

Thus,  

∴ Percentage increase in the volume of the wire is  

= 0.006 * 100%  

= 0.6 %

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