Question

A copper rod of $88 \,cm$ and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is $(a_{C_{u}}=1.7 \times 10^{-5}\,K^{-1}$ and $\left.a_{A_{l}}=2.2 \times 10^{-5} K^{-1}\right)$

• A. 88 cm
• B. 68 cm
• C. 6.8 cm
• D. 113.9cm

Answer 1

Answer: (B)

68 cm

Answer 2

$\Delta\,l_{1}=\Delta \,l_{2}$
$l_{1} \propto_{1} \Delta \theta=l_{2} \propto_{2} \Delta \,\theta$
$88 \times 1.7 \times 10^{-5}=l_{2} \times 2.2 \times 10^{-5}$
$\Delta I_{2}=88 \times 1.7 / 2.2=68 \,cm$