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What force would be required to stretch ...

What force would be required to stretch a streel wire fo `4 mm^2` cross section, so that its length becomes 3 times its original length ? Given that Young's modulus of the meterial of the steel wire is `2.4 xx 10^(12) dyne // cm^2.`

Text Solution

Verified by Experts

The correct Answer is:
`1.92 xx 10^(11) dyn e`
Here `F =?, A = 4 mm^2 =4xx10^(-2) cm^2 ,` increase in length `Delta l = 3l - l = 2l,`
`Y = 2.4 xx 10^(12) dyn e//cm^2`
As `Y = (F)/(A) (l)/(Delta l)`
or `F = (YA Delta l)/(l) = ((2.4 xx10^(12))xx(4xx10^(-2))xx2l)/(l)`
`(2.4 xx 4xx2xx10^(10)`
`=19.2 xx10^(10) = 1.92 xx 10^(11) dyn e`
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Knowledge Check

  • The force required to stretch a steel wire 100m^(2) a section to triple its length is (Y= 2xx 10^(11)Nm^(-2))

    A
    `4 xx 10^(10)N`
    B
    `4 xx 10^(12)N`
    C
    `4 xx 10^(11)N`
    D
    `4 xx 10^(13)N`

  • What is the force requiredto stretch a steel wire of 1 cm^(2) cross-section to 1.1 times its length ? (Y = 2 xx 10^(11) N//m^(2))

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

  • The force required to stretch a steel wire 1cm^(2) in cross - section to increase its length by 1% ,if its Young's modulus is 2xx10^(11)Nm^(-2) ,is

    A
    `10^(5)N`
    B
    `3xx10^(5)N`
    C
    `2xx10^(5)N`
    D
    `4xx10^(5)N`

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