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If Young.s modulus of the material of a...

If Young.s modulus of the material of a wire is `1.2xx10^(11) Nm^(-2)` , calculate the work done in stretching the wire of length 3 m and cross-sectional area `4mm^(2)` when it is suspended vertically and a load of 8 kg is attached to its lower end.

Text Solution

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`Y=1.2xx10^(11)Nm^(-2) , L=3m`,
`A=4mm^(2)=4xx10^(-6)m^(2), M=8kg`.
work done `=(1)/(2)xx` stretching force `xx` increase in length.
But increase in length, `e=(FL)/(AY)`
The work done `=(1)/(2)xx(F^(2)L)/(AY) = (1)/(2) xx ((Mg)^(2)L)/(AY)`
`=(1)/(2) xx ((8xx9.8)^(2)xx3)/( 4xx10^(-6) xx 1.2xx10^(11)) =0.0192 J`
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