A steel sheet at `20^(@)C` has the same surface area as a brass sheet at `10^(@)C` . If the coefficient of linear expansion of steel is `11xx10^(-6)//K` and that of bross is `19xx10^(-6)//K` , the common temperature at which both the sheets would have the same surface area is

Options

A. `3.75^(@)C`
B. `-3.75^(@)C`
C. `7.5^(@)C`
D. `-7.5^(@)C`

Answer

B

Explanation

For area
`Atheta=Atheta_(0)[1+beta(theta-theta_(0))=Atheta_(0)[1+2alpha(theta-theta_(0))]`
`(A_(s))_(theta)=(A_(s))_(20)[1+2alpha_(s)(theta-20)]`
`(A_(b))_(theta)=(A_(b))_(10)[1+2alpha_(b)(theta-10)]`
Given `(A_(s))_(theta)=(A_(b))_(theta)` and `(A_(s))_(20)=(A_(b))_(10)`
`alpha_(s)(theta-20)=alpha_(b)(theta-10)`
`11theta-220=19theta-190`
`8theta=-30 implies theta=-3.75^(@)C` .