a mild steel bar of length 10cm and width of 10mm is extended by 0.01 mm. Which of the following is equal to the change in width of the bar.(The Poisson's ratio of mild steel is 0.31)
A 3.1x10-4mm
B -3.1x10-4mm
C 3.1x10-5mm
D -3.1x10-5mm
To find the change in width of the mild steel bar, we can use the formula for lateral strain, which is given by:
lateral strain = -Poisson's ratio * longitudinal strain
Here, the longitudinal strain is given by the change in length divided by the original length. In this case, the change in length is 0.01 mm and the original length is 10 cm (or 100 mm).
longitudinal strain = change in length / original length
= 0.01 mm / 100 mm
= 0.0001
Now we can substitute the values into the formula to find the lateral strain:
lateral strain = -0.31 * 0.0001
= -0.000031
The lateral strain is negative because the bar experiences a decrease in width.
Finally, to find the change in width, we can multiply the lateral strain by the original width of the bar, which is 10 mm:
change in width = lateral strain * original width
= -0.000031 * 10 mm
= -0.00031 mm
Therefore, the correct answer is B) -3.1x10^-4 mm.