Question

A brass scale is graduated at ${10}^{\circ }C$. What is the true length of a zinc rod which measures 60.00 cm on this scale at ${30}^{\circ }C$? Linear expansively of brass = $18\times {10}^{-6}{K}^{-1}$.

• A. 60.02 cm
• B. 60.2 cm
• C. 61.02 cm
• D. 60.0002 cm

Answer 1

The correct option is A 60.02 cm

Since the scale is graduated at ${10}^{\circ }C$,
1 cm of the scale at ${10}^{\circ }C$ = exactly 1 cm
$\therefore$ 1 cm of the scale at ${30}^{\circ }C$
$=exactly(1+18\times {10}^{-6}\times 20)cm$
$\therefore$ 60 cm of the scale at ${30}^{\circ }C$
$=exactly60.00(1+36\times {10}^{-5})$
$=60.02cm$