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The speed of a transverse wave going on...

The speed of a transverse wave going on a wire having a length 50 cm and maas 5.0 g is `80ms^(-1)` The area of cross section of the wire is `1.0mm.^2` and its Young modulus is `16 xx 10^(11) N m^(-2).` Find the extension of the wire over its natural lenth.

Text Solution

Verified by Experts

The linear mass density is `mu=(5xx10^(-3)kg)/(50xx10^(-3)m)=1.0xx10^(-2) kg//m`
The wave speed is `v=sqrt(F)//(mu)`
Thus, the tension is `F=muv^(2)=(1.0xx10^(-2)(kg)/(m))xx6400(m^(2))/(s^(2))=64 N`
young's modulus is given by `Y=(F//A)/(DeltaL//L)`
The extension is, therefore,
`DeltaL=(FL)/(AY)=(64xx0.50)/((1.0xx10^(6))xx(8xx10^(11)))=0.04 mm`
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Knowledge Check

  • The area of a cross-section of steel wire is 0.1 cm^(-2) and Young's modulus of steel is 2 x 10^(11) N m^(-2) . The force required to stretch by 0.1% of its length is

    A
    1000 N
    B
    2000 N
    C
    4000 N
    D
    5000N

  • The area of a cross section of steel wire is 0.1cm^2 and Young's modulus of steel is 2xx10^(11)Nm^-2 . The force required to strech by 0.1% of its length is

    A
    `1000N`
    B
    `2000N`
    C
    `4000N`
    D
    `5000N`

  • The time taken by a transverse wave going on a wire having mass 5 g, form one end to another end of wire is 0.5 s. The area of cross-section fo wire is 1 mm^(2) and Young's modulus of elasticity is 16 xx 10^(11) N//m^(2) . The speed of wave is 80 m/s. The strain in wire is

    A
    `5 xx 10^(-7)`
    B
    `2 xx 10^(-7)`
    C
    `3 xx 10^(-6)`
    D
    `4 xx 10^(-6)`