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JEE Main 202229 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Evening Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2022 · 29 June · Evening Shift · Physics · Thermal Properties of Matter

At what temperature a gold ring of diameter 6 . 230cm be heated so...

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 \left(27 ° C\right).<br/>(Given:coefficientoflinearthermalexpansionofgold.<br />(Given: coefficient of linear thermal expansion of gold{\alpha}_{L} = 1 . 4 \times {10}^{- 5}{K}^{- 1}$)

Options

  1. A125.7°C125 . 7 ° C
  2. B91.7°C91 . 7 ° C
  3. C425.7°C425 . 7 ° C
  4. D152.7°C152 . 7 ° C

Correct answer

D. 152.7°C152 . 7 ° C

Step-by-step solution

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+α\DeltaT]l = {l}_{0}\left[1 + \alpha\DeltaT\right]

⇒6.241=6.230[1+1.4×10−5(T−27)]⇒ 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)⇒ \dfrac{6 . 241}{6 . 230} - 1 = 1 . 4 \times {10}^{- 5}\left(T - 27\right)

⇒T=152.7°C⇒ T = 152 . 7 ° C

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