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 ration of the material of the rod is 0.3)

Options

A. 0.03
B. 0.01
C. 0.007
D. 0.004

Answer

D

Explanation

Let volume of the rod be V.

` therefore V = xyz`
Now change in volume is
`(dV)/(V) = (dx)/(x) + (dy)/(y) + (dz)/(z)`
`(dV)/(V) = (dl)/(l) - mu (dl)/(l) - mu (dl)/(l) = (1 - 2mu)(dl)/(l)` …(i0
Stress = young.s modulus (Y) x strain
As stress = 1% of Y = 0.01 Y
` therefore 0.01 Y = Y xx (dl)/(l)`
from eqn(i)
`(dV)/(V) = (1-2 xx 0.3) xx 0.01 " " [ because mu = 0.3 "and " (dl)/(l) = 0.01 ]`
` rArr (dV)/(V) = 0.01 xx 0.4 = 0.4%`