Question

(A): A meter scale measures correct lengths at 0C. Using this scale, the length of an object is measured as 15 m at 40C. Then the correct length of that object is 15.012 m $(\alpha =20\times {10}^{-6}{/}^{\circ }C)$ .
(B): True length $=$ scale reading

• 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 C A is true and B is false

$\Delta L+L$ is expanded the length of the meter scale. now the initial reading was L.
therefore,
we need to find actual length of L which is given by $\Delta L+L$
Therefore, $\Delta L+L=L(1+\alpha \Delta \theta )$
$=15(1+20\times {10}^{-6}\times 40)$
$=15(1+8\times {10}^{-4})$
$=15\times 1.0008$
$=15.012$
Therefore, actual reading was 15.012m
Hence A is correct but reason is not correct because true length is not the scale reading always