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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 (27°C). (Given: coefficient of linear thermal expansion of gold α_L = 1.4 × 10⁻⁵ K⁻¹)

1. 125.7°C
2. 91.7°C
3. 425.7°C
4. 152.7°C

Correct answer: 152.7°C

Solution

The correct option is right because it accurately calculates the required temperature increase to expand the gold ring's diameter from 6.230 cm to match the wooden bangle's diameter of 6.241 cm, using the formula for linear thermal expansion. By applying the coefficient of linear thermal expansion for gold, the resulting temperature of 152.7°C ensures the ring expands sufficiently to fit over the bangle.

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