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The volume of a block of a metal changes...

The volume of a block of a metal changes by `0.12%` when it is heated through `20^(@)C` . The coefficient of linear expansion of the metal is

A

`4 xx 10^(-5)"^(@) C^(-1)`

B

`2 xx 10^(-5)"^(@) C^(-1)`

C

`0.5 xx 10^(-5)"^(@) C^(-1)`

D

`4 xx 10^(-4)"^(@) C^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `(DeltaV)/(V) = 0.12%, = (0.12)/(100)`
`DeltaT = 20 .^(@)C`
Now, `gamma = (DeltaV)/(VDeltaT) = (0.12)/(100 xx 20) = 6 xx 10^(-5) .^(@)C^(-1)`
`:. alpha = (gamma)/(3) = 2 xx 10^(-5) .^(@)C^(-1)`
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Knowledge Check

  • The volume of a block of a metal changes by 012% when it is heated through 20^(@)C . The coefficient of linear expansion of the metal is

    A
    `2.0xx10^(-5)per^(@)C`
    B
    `4.0xx10^(-5)per^(@)C`
    C
    `6.0xx10^(-5)per^(@)C`
    D
    `8.0xx10^(-5)per^(@)C`

  • The volume of a metal sphere increases by 0.24% when its temperature is raised by 40^(@)C . The coefficient of linear expansion of the metal is .......... .^(@)C

    A
    `2xx10^(-5)`
    B
    `6xx10^(-5)`
    C
    `2.1xx10^(-5)`
    D
    `1.2xx10^(-5)`

  • The volume of a solid decreases by 0.6% when it is cooled through 50^(@)C . Its coefficient of linear expansion is

    A
    `4xx10^(-6) K`
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    `5xx10^(-5) K`
    C
    `6xx10^(4)K`
    D
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