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The volume of a metal sphere increases b...

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

A

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

B

`6 xx 10^(-5).^(@)C^(-1)`

C

`18 xx 10^(-5).^(@)C^(-1)`

D

`1.2 xx 10^(-5).^(@)C^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
From, `V_(T) = V_(0)(1+gammaDeltaT)`
`rArr (V_(T) -V_(0))/(V_(0)) = gammaDeltaT`
`(0.24)/(100) = gamma40 .^(@)C`
`gamma = (0.24)/(100 xx 40) = 6 xx 10^(-5) .^(@)C^(-1)`
Coefficient of linear expansion,
`alpha = (gamma)/(3) = (6 xx 10^(-5))/(3) = 2 xx 10^(-5) .^(@)C^(-1)`
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