Thermal Properties of Matter

JEE Main level, numerical answer, medium

21 of 126

Question 21 of 126

A hole is drilled in a metal sheet. At 27∘C27^{\circ}C, the diameter of hole is 5cm5cm. When the sheet is heated to 177∘C177^{\circ}C, the change in the diameter of hole is d×10−3cmd\times {10}^{-3}cm . The value of dd will be _____, if coefficient of linear expansion of the metal is 1.6×10−5/C∘1.6\times {10}^{-5}/C^{\circ}

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Answer: 12

Expansion of hole will be similar to that of an imaginary disc.
Let diameter be d0{d}_{0} at 27∘C27^{\circ}C and d′{d}^{'} at 177∘C177^{\circ}C. Therefore, we can write
d′=d0(1+αΔT){d}^{'}={d}_{0}\left(1+\alpha \Delta T\right)
Therefore, change in diameter will be
⇒d′−d0=(5)×(1.6×10−5)×(177−27)\Rightarrow {d}^{'}-{d}_{0}=\left(5\right)\times \left(1.6\times {10}^{-5}\right)\times \left(177-27\right)
=12×10−3cm=12\times {10}^{-3}cm
Hence, required value of d=12d=12.

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