If the stress on a wire is 10\(^7\)Nm\(^{-2}\) and the wire is stretched from its original length of 10.00 cm to 10.05 cm. The Young's modulus of the wire is
A
5 . 0 x 104 Nm-2
B
5 . 0 x 105 Nm-2
C
2 . 0 x 108 Nm-2
D
2 . 0 x 109 Nm-2
Verified Correct Answer: D.
Physical Principles & Numerical Solution
Y = \(\frac{\text{stress}}{\text{strain}}\), but stress = 10\(^7\)Nm\(^{-2}\) (given).
Strain = \(\frac{\text{e}}{l_o}\). = \(\frac{(0.1005 - 0.100)}{0.1}\) = 0.005m
Thus Y = \(\frac{10^7}{0.005}\) = 2.0 x 10\(^9\)Nm\(^{-2}\)
(NOTE: cm → m)
Source: Myschool Past Questions Archive (Record #325)