Wave Mechanics Question 528
Question: The Young’s modulus of the material of a wire is $ 2\times 10^{10}N{{m}^{-2}} $ . If the elongation strain is 1 %, then the energy stored in the wire per unit volume in $ J{{m}^{-3}} $ is
Options:
A) $ 10^{6} $
B) $ 10^{8} $
C) $ 2\times 10^{6} $
D) $ 2\times 10^{8} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ Y=2\times 10^{10}N{{m}^{-2}};\frac{\Delta l}{l}=0.01 $ Work done per unit volume $ =\frac{1}{2}\times stress\times strain=\frac{1}{2}\times Y\times strain^{2} $
$ =\frac{1}{2}Y{{( \frac{\Delta l}{l} )}^{2}} $
$ \
Therefore U=\frac{1}{2}\times 2\times 10^{10}\times {{( \frac{1}{100} )}^{2}}=U=10^{6}J{{m}^{-3}} $
BETA
