The volume of a metal sphere increases by `0 cdot 24%` when its temperature is raised by `40^(@)C`. The coefficient of linear expansion of the metal is…`""^(@)C^(-1)`:

Options

A. `2xx10^(-5)`
B. `18xx10^(-5)`
C. `6xx10^(-5)`
D. `1 cdot2 xx10^(-5)`

Answer

A

Explanation

`V=V_(0)(1+gamma Delta T)`
`rArr gamma =(V-V_(0))/(V_(0) Delta T)=(0 cdot 24)/(100xx40)=6xx10^(-5)""^(@)C^(-1)`
Now `alpha =(gamma)/(3) =2xx10^(-5)^""(@)C^(-1)`
`therefore` Correct choice (a).