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

Options

A. 0.1mm
B. 0.2mm
C. 0.3mm
D. 0.4mm

Answer

C

Explanation

`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