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The amount of elastic potential energy per unit volume (in SI unit) of a steel wire of length 100 cm to stretch it by 1 mm is (if Young's modulus of the wire = $2.0\times10^{11}\ Nm^{-2}$):
A
$10^{11}$
B
$10^{17}$
C
$10^7$
D
$10^5$
Detailed Solution
$\dfrac{E.P.E}{Volume}=\dfrac{1}{2}(stress)(strain)=\dfrac{1}{2}(Y)(strain)^2=\dfrac{1}{2}(Y)\left(\dfrac{\Delta L}{L}\right)^2=\dfrac{1}{2}(2\times10^{11})\left(\dfrac{1\times10^{-3}}{100\times10^{-2}}\right)^2=10^5$.