JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
At what temperature (in \( ^{\circ} C\)) 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 \(125.7\)
- B \(91.7\)
- C \(425.7\)
- D \(152.7\)
Answer & Solution
Correct Answer
(D) \(152.7\)
Step-by-step Solution
Detailed explanation
\(\Delta \ell=6.241-6.230=0.011 \,cm\) \(\Delta \ell=\ell \alpha \Delta \theta\) \(0.011=6.230 \times 1.4 \times 10^{-5}(\theta-27)\) \(\theta-27=\frac{0.011 \times 10^{5}}{6.230 \times 1.4}\) \(\theta \approx 153.11\) nearest is \(152.7^{\circ} C\)
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