JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Heat & Thermodynamics

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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 (

2 7^{\circ} C

).
(Given: coefficient of linear thermal expansion of gold

α_{L} = 1.4 \times 1 0^{- 5} K^{- 1}

)

(A) $125. 7^{\circ} C$
(B) $91. 7^{\circ} C$
(C) $425. 7^{\circ}$
(D) $152. 7^{\circ} C$ ✓ Correct

Answer: (D)

Solution

The gold ring must expand to match the bangle diameter.

Change in diameter:

Δ ℓ = 6.241 - 6.230 = 0.011

cm.

Using linear thermal expansion:

Δ ℓ = ℓ α Δ T

0.011 = 6.230 \times 1.4 \times 1 0^{- 5} \times (θ - 27)

(θ - 27) = \frac{0.011}{6.230 \times 1.4 \times 1 0 ^{- 5}} = \frac{1100}{6.230 \times 1.4} \approx 126.1

θ \approx 153. 1^{\circ} C

The nearest option is (D)

152. 7^{\circ} C

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Heat & Thermodynamics

Solution

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