At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C).

**(Given : coefficient of linear thermal expansion of gold a_L = 1.4 * 10^-⁵ K^-¹)**

Option 1 - 125.7°C

Option 2 - 91.7°C

Option 3 - 425.7°C

Option 4 - 152.7°C

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Answered by

Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 4

Detailed Solution:

According to question, we can write

$d = d_{0} (1 + α Δ T) \Rightarrow 6.241 = 6.230 (1 + 1.4 * 1 0^{- 5} * Δ T)$

$\Rightarrow T = 126.18 + 27 = 153.18 ° C$

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At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C). (Given : coefficient of linear thermal expansion of gold aL = 1.4 * 10-5 K-1)