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The stress along the length of a rod (wi...

The stress along the length of a rod (with rectangular cross section) is 1% of the Young's modulus of its material. What is the approximate percentage of change of its volume ? (Poisson's ratio of the material of the rod is 0.3)

A

0.03

B

0.01

C

`0.7%`

D

`0.4%`

Text Solution

Verified by Experts

The correct Answer is:
D
Let volume of rod =V=xyz and Young.s modulus of its material of the rod =Y
Now, `F/A=Y times 1%`
or, `Y times (Delta x)/x=Y/100`
or, `(Deltax)/x=0.01`
`therefore(DeltaV)/V=(Deltax)/x+(Deltay)/y+(Deltaz)/z`
`=(Deltax)/x-sigma (Deltax)/x-sigma(Deltax)/x`.....(1)
[`because` Poisson.s ratio,
`sigma=(lateral strai n)/(longitudi nal strai n)=((Deltay)/y)/((Deltax)/x)=((Deltaz)/z)/((Deltax)/x)`]
Negative symbol in equation (1) implies that ,as length increase dut to stress, value of y and z decreases simulataneously.
`therefore` From equation (1)
`(DeltaV)/V=0.01-2times0.3times 0.01=0.004=0.4%`
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