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The pressure that has to be applied to t...

The pressure that has to be applied to the ends of a steel wire of length 10cm to keep its length constant when its temperature is raised by `100^@C` is : (For steel Young's modulus is `2xx10^11 Nm^-2` and coefficient of thermal expansion is `1.1xx10^-5K^_1`)

A

`2.2xx10^8Pa`

B

`2.2xx10^9Pa`

C

`2.2xx10^7Pa`

D

`2.2xx10^6Pa`

Text Solution

Verified by Experts

The correct Answer is:
A
(a) Young's modulus Y=stress/strain
`stress=Yxxstrain`
Stress in steel wire =Applied pressure
`Pressure=stress=Yxxstrain`
`Strain=(DeltaL)/L= alphaDeltaT` (As length is constant)
`=2xx10^11xx1.1xx10^-5xx100`
`=2.2xx10^8Pa`
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Knowledge Check

  • A steel rod of length 1 m is heated from 25^@ "to" 75^@ C keeping its length constant. The longitudinal strain developed in the rod is ( Given, coefficient of linear expansion of steel = 12 xx 10^-6//^@ C ).

    A
    `6 xx 10^-4`
    B
    `-6 xx 10^-5`
    C
    `-6 xx 10^-4`
    D
    zero

  • 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`

  • What is the work done per unit volume when a steel wire is stretched by 0.2% of its original length ? (Young's modulus of steel is 2xx10^(11)N//m^(2) )

    A
    `2xx10^(5)J//m^(3)`
    B
    `4 xx 10^(5)J//m^(3)`
    C
    `1//2 xx 10^(5)J//m^(3)`
    D
    `3//4 xx 10^(5) J//m^(3)`

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