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

A steel sheet at `20^(@)C` has the same surface area as a brass sheet

1.	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 isA. `3.75^(@)C`B. `-3.75^(@)C`C. `7.5^(@)C`D. `-7.5^(@)C`
Answer» Correct Answer - B 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` .

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