Question

A tape measures the length of a copper rod as $90\text{cm}$ at ${10}^{\circ }C$. What would the tape read for the length of the rod at ${30}^{\circ }C$?
Given, ${\alpha }_{\text{Cu}}=1.7\times {{10}^{-5}}^{\circ }{C}^{-1}$

• A. $90\text{cm}$
• B. $90.01\text{cm}$
• C. $90.3\text{cm}$
• D. $90.03\text{cm}$

Answer 1

The correct option is D $90.03\text{cm}$

Given:
Length of copper rod at ${10}^{\circ }C$
$L_0=90\text{cm}$
At ${30}^{\circ }C$,
Length of copper rod $L=L_0(1+{\alpha }_c\Delta T)\text{cm}$
$=90(1+1.7\times {{10}^{-5}}^{\circ }{C}^{-1}\times {20}^{\circ }C)$
$=90.03\text{cm}$