Question

statement (1): To have the same difference between the lengths of two metallic rods their initial lengths of 0C should be in the inverse ratio of their coefficient of linear expansion.
statement (2): If the lengths of two metallic rods at 0 Care in the inverse ratio of their coefficient of linear expansion then the change in the lengths due to the same rise of temperature is the same.

• A. statement 1 and statement 2 are correct and statement 2is correct explanation for statement 1
• B. statement 1 and statement 2 are correct and statement 2 is not correct explanation for statement 1
• C. statement 1 is true and statement 2 is false
• D. statement 1 is wrong and statement 2 is true.

Answer 1

The correct option is A statement 1 and statement 2 are correct and statement 2is correct explanation for statement 1

We know that,
$\Delta L=\alpha L\Delta \theta$
to keep change in length same for two different rods
$\alpha L=constant$
therefore,
${\alpha }_1{L}_1={\alpha }_2{L}_2$
${\alpha }_1/{\alpha }_2=L_2/L_1$
inverse ratio of the initial lengths of the rods should be equal to the ratio of their coefficient of linear expansion.
Since statement 2 is correct explanation therefore, option (A) is correct