The area of a circular copper coin increases by 0.4 % when its temperature is raised by `100^(@)C`. The coefficient of linear expansion of the coin is :

Options

A. `1xx10^(-5)//^(@)C`
B. `2 xx10^(-5)//^(@)C`
C. `3xx10^(-5) //^(@)C`
D. `4xx10^(-5)//^(@)C`

Answer

B

Explanation

Given, area of a circular copper coin increases by 0.4 %
i.e., `(Delta A)/A =0.004`
Increase in temperature, `Delta T=100^(@)C`
We know that, the coefficient of areal expansion `beta` is given by
`beta=((Delta A)/A).1/(Delta T)=0.004/100=4xx1-^(-5)//^(@)C`
`:.` Coefficient of linear expansion, of the coin is
`alpha=beta/2=(4xx10^(-5))/2 //^(@)C=2xx10^(-5)//^(@)C`