Question

(A): the linear expansion of metal wire is $1$% when it is heated from $T_1$to $T_2$ (in ${}^{o}C$). id a thin plat of same metal of dimension $2L\times L$ was heated from $T_1$ to $T_2$, then the areal expansion is $3$%.

(B): the percentage of areal expansion $=2\times$ % linear expansion. The % expansion are independent of original dimensions.

• A. A and B are correct and B is correct explanation for A
• B. A and B are correct and B is not correct explanation for A
• C. A is true and B is false
• D. A is wrong and B is true.

Answer 1

The correct option is D A is wrong and B is true.

Since linear expansion will occur in both length and breadth of the cross-section therefore, a 1% increase in length will occur and a 1% increase in breadth will occur.
Therefore, $\Delta A=(l+\Delta l)(b+\Delta b)-lb$
$\Delta A=b\Delta l+l\Delta b+\Delta l\Delta b$
percentage increase in area will be $\Delta A/A=\Delta A/lb=\Delta l/l+\Delta b/b+\Delta l\Delta b/lb=0.01+0.01+0.01\times 0.01$
$\Delta A/A=0.0201=0.02$
Therefore, percentage increase in surface area will be 2 %
Therefore, A is wrong. and reason is correct statement when we apply the approximations.