A steel wire of length 2 m and Young's modulus 
is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and 
respectively, then the elastic potential energy density of the wire is 
(in SI units).
Text Solution
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To find the elastic potential energy density of the steel wire, we need to use the given information and formulae for strain and energy density.
Given:
The length of the wire, 
Young's modulus, 
Poisson's ratio, 
Transverse strain, 
The formula for Poisson's ratio is:
From this, we solve for the longitudinal strain 
:
Substitute the given values:
The elastic potential energy density 
is given by:
where 
. Plug in the values:
Simplify further:
Thus, the elastic potential energy density of the wire is 
SI units.
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