Speed of transwerse wave of a straight wire having mass 6.0g length 60cm and area of cross- section 1.0 mm^(2) is 90 m/s. If the Young's modulus of wire is 1.6 xx 10^(11) Nm^(-2), the extension of wire over its natural length is

Speed of transwerse wave of a straight wire having mass 6.0g length 60

1.	Speed of transwerse wave of a straight wire having mass 6.0g length 60cm and area of cross- section 1.0 mm^(2) is 90 m/s. If the Young's modulus of wire is 1.6 xx 10^(11) Nm^(-2), the extension of wire over its natural length is
Answer» 0.1mm 0.2mm 0.3mm 0.4mm Solution :`M= 6g m = 6 xx 10^(-3) kg` `L= 60cm = 0.6m` `A=1 mm^(2) = 1 xx 10^(-6) m^(2)` `v= SQRT((T)/(mu)) RARR v^(2) = (T)/(mu)` `:. V^(2) = (T)/(10^(-2)) [ :. mu= (M)/(L) = (6 xx 10^(-3))/(0.6) = 10^(-2) (kg)/(m)]` `:. T= (10)^(-2) v^(2)` `=(10)^(-2) xx (90)^(2)= 81N` Now Young.s modulus `y= ("stress")/("Strain") = (T//A)/(DeltaL//L)` `:. y= (TL)/(Delta LA)` `:. Delta L= (T L)/(Ay) = (81 xx 0.6)/(1 xx 10^(-6) xx 1.6 xx 10^(11))` `=30.375 xx 10^(-5m)` `=0.30375 xx 10^(-3m)` =0.3mm