Question

A rod is measured using a scale. The reading is $60\text{cm}$ at ${12}^{\circ }\text{C}$. If thermal coefficient of linear expansion of the rod is $3\times {10}^{-5}{/}^{\circ }\text{C}$, the reading of the rod at ${42}^{\circ }\text{C}$ is:
(Assume the scale does not expand)

• A. $60.025\text{cm}$
• B. $60.054\text{cm}$
• C. $60.065\text{cm}$
• D. $59.985\text{cm}$

Answer 1

The correct option is B $60.054\text{cm}$

The increment in length
$=\alpha l\Delta T$
$=3\times {10}^{-5}\times 60\times (42-12)$
$=3\times {10}^{-5}\times 60\times 30$
$=54\times {10}^{-3}\text{cm}$
$=0.054\text{cm}$
So, total length $=(60+0.054)\text{cm}$
$=60.054\text{cm}$