Question

If this aluminum rod measure a length of steel as 88.42 cm at ${35}^{\circ }C$, what is the correct length of the steel at ${35}^{\circ }C$ ?

• A. $44.49cm$
• B. $58.49cm$
• C. $88.49cm$
• D. $77.49cm$

Answer 1

The correct option is C $88.49cm$

The error in measuring distance will be equal to the length expansion corresponding to the measured length. Hence,

$e=\Delta l=88.42\left({\alpha }_{Al}\right)\Delta T$

$e=88.42\left(24X{10}^{-6}\right)(35-5)cm\approx 0.064cm$

Since at higher temperature, distance between markings on scale will increase, hence actual length will be more than the measured length. Hence, correct length of steel rod at this temperature will be

$L=L^{\prime }+e=88.42+0.064cm\approx 88.49cm$

Answer is $88.49cm$