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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 10 cm to keep its length constant when its temperature is raised by `100^(@)C` is (For steel, Young's modulus is `2 times 10^(11)N*m^(-2)` and coefficient of linear expansion is `1.1 times 10^(-5)K^(-1))`

A

`2.2 times 10^(8)Pa`

B

`2.2 times 10^(9)Pa`

C

`2.2 times 10^(7)Pa`

D

`2.2 times 10^(6)Pa`

Text Solution

Verified by Experts

The correct Answer is:
A
As length is constant,
strain `=(DeltaL)/L=alphaDeltaQ`
Now, pressure = stress = Y `times` strain
`" "=2 times 10^(11) times 1.1 times 10^(-5) times 100`
`" "=2.2 times 10^(8)Pa`
The option (A) is correct.
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Knowledge Check

  • The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100^@C is (For steel Young's modulus is 2 xx 10^11 Nm^-2 and coefficient of thermal expansion is 1.1 xx 10^-5 K^-1 )

    A
    `2.2xx10^8Pa`
    B
    `2.2xx10^9Pa`
    C
    `2.2xx10^7Pa`
    D
    `2.2xx10^6Pa`

  • The length of each steel rail of a line at 10^(@)C is 25 m. What gap should be maintained between two successive rails so that up to 50^(@)C they will not be strained? [coefficient of linear expansion of steel =11 times 10^(-6@)C^(-1) ]

    A
    5.5 mm
    B
    8.25 mm
    C
    11 mm
    D
    1.65 mm

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