Question

At what temperature a gold ring of diameter $6.230\,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241\, cm$ ? Both the diameters have been measured at room temperature $\left(27^{\circ} C \right)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{ L }=1.4 \times 10^{-5} K ^{-1}$ )

• A. $125.7^{\circ} C$
• B. $91.7^{\circ} C$
• C. $425.7^{\circ}$
• D. $152.7^{\circ} C$

Answer 1

Answer: (D)

$\Delta \ell=6.241-6.230=0.011\, cm$
$\Delta \ell=\ell \alpha \Delta \theta$
$0.011=6.230 \times 1.4 \times 10^{-5}(\theta-27)$
$\theta-27=\frac{0.011 \times 10^{5}}{6.230 \times 1.4}$
$\theta \approx 153.11$ nearest is $152.7^{\circ} C$.