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A steel wire of 4.0 m is stretched throu...

A steel wire of 4.0 m is stretched through 2.0 mm. The cross - sectional area of the wire is `2.0 mm^2.` If young's modulus of steel is `2.0 xx10^(11) Nm^(-2)` find (i) the energy density of the wire, (ii) the elastic potential energy stored in the wire.

Text Solution

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Here, `l=4.0m, Deltal=2xx10^(-3)m, a=2.0xx10^(-6)m^(2), Y=2.0xx10^(11)Nm^(-2)`
(i) The energy density of stretched wire
`(DeltaU)/("Volume")=(1)/(2)"stress"xx"strain"`
`=(1)/(2)xxYxx"(strain)"^(2)`
`=(1)/(2)xx2.0xx10^(11)Nm^(-2)xx((2xx10^(-3))/(4))^(2)`
`=2.5xx10^(4)J//m^(3)`
(ii) Elastic potential energy = energy density `xx` volume
`=(2.5xx10^(4)J//m^(3))xx(8.0xx10^(-6)m^(3))`
`=0.20J`
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