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)

Length and cross sectional area of a wire are 5 m and 2.5 mm^(2). Calc

1.	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)
Answer» Solution :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`