Length and cross sectional area of a wire are 5 m and `2.5 mm^(2).` Calculate work required to be done to increase its length by 1 mm. Young's modulus of material of wire `=2 xx 10 ^(11) Nm ^(-2)`

Explanation

Here l = 5m
`Delta l = 1mm = 10 ^(-3) m`
`A = 2.5 mm ^(2) =2.5 xx 10 ^(-6) m ^(2)`
`Y=2 xx 10 ^(11) Nm ^(-2)`
Work to be done
`W = 1/2` stress `xx` strain `xx` volume
`=1/2 xx Y xx (epsi_(l)) ^(2) xx Al`
`1/2 xx` Young modulus
but `epsi _(l) =(Delta l )/(l) = (10 ^(-3))/(5) and `
volume `V = Al = 2.5 xx 10 ^(-6) xx 5 = 12.5 xx 10 ^(-6) m^(3)`
`therefore W -1/2 xx 2 xx 10^(11) xx (( 10 ^(-3))/( 5 )) ^(2) xx 12.5 xx 10 ^(-6) `
`= 10 ^(11) xx (10 ^(-6))/(25) xx 12.5 xx 10 ^(-6)`
`= 0.5 xx 10 ^(-1)`
`therefore W =5 xx 10 ^(-2) J`