A wire of radius 0.2 mm is extended by 0.5% of its length when supported by a load of 1.5 kg. Determine the Young's modulus for the material of the wire.
[Take g = 10 ms\(^{-2}\)]
A
\(2.4×10^{10}(Nm^{-2})\)
B
\(1.5×10^{10}(Nm^{-2})\)
C
\(2.4×10^9(Nm^{-2})\)
D
\(1.3×10^{10}(Nm^{-2})\)
Verified Correct Answer: A.
Physical Principles & Numerical Solution
r=0.2mm = \(2 \times {10^{-4}}\) e= 0.05% of L,=0.005L, m=1.5kgg=\(10 ms^{-2}\) , y=?,
(1000 mm = 1m)
Y = \(\frac{FL}{Ae}\)
w = mg = 1.5 \times 10 = 15
A = \(\pi r^2\) = \(\frac{22}{7}\times(2\times10^{-4})^2\) = \(1.26\times10^{-7}(m^2)\)
⇒ Y = \(\frac{15L}{1.26\times10^{-7}\times0.005L}\)
⇒ Y = \(\frac{15}{1.26\times10^{-7}\times0.005}\)
⇒ Y = \(\frac{15}{6.29\times10^{-10}}\)
Y = \(2.4\times10^{10}(Nm^{-2})\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #67743)