Thermal Properties of Matter

JEE Main level, single correct, medium

23 of 126

Question 23 of 126

At what temperature a gold ring of diameter 6.230cm6.230cm be heated so that it can be fitted on a wooden bangle of diameter 6.241cm6.241cm? Both the diameters have been measured at room temperature (27∘C)\left(27^{\circ}C\right).
(Given: coefficient of linear thermal expansion of gold αL=1.4×10−5K−1{\alpha }_{L}=1.4\times {10}^{-5}{K}^{-1})

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Answer: (D) 152.7∘C152.7^{\circ}C

To fit gold ring of diameter 5.230cm5.230cm over wooden bangle of diameter 6.241cm6.241cm, gold ring expansion is required.
So, l=l0[1+αΔT]l={l}_{0}\left[1+\alpha \Delta T\right]
⇒6.241=6.230[1+1.4×10−5(T−27)]\Rightarrow 6.241=6.230\left[1+1.4\times {10}^{-5}\left(T-27\right)\right]
⇒6.2416.230−1=1.4×10−5(T−27)\Rightarrow \dfrac{6.241}{6.230}-1=1.4\times {10}^{-5}\left(T-27\right)
⇒T=152.7∘C\Rightarrow T=152.7^{\circ}C

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