At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A… | JEE Main 2019 (12 Apr, Shift 1)

Q63JEE Main 2019 · 12 APR · SHIFT 1Difficult

Thermometry & Thermal Expansion

At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value of M is close to: (Coefficient of linear expansion and Young’s modulus of brass are 10–5 /oC and 1011 N/m 2, respectively; g= 10 ms–2)

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Answer: (c)

Stretch by the load equals thermal contraction: $\dfrac{Mg}{\pi r^2 Y} = \alpha\Delta\theta$ .
$M = \dfrac{Y\pi r^2\alpha\Delta\theta}{g} = \dfrac{10^{11} \times \pi \times 10^{-6} \times 10^{-5} \times 20}{10}$
$M = 2\pi \approx 6.3$ kg; the closest option is 9 kg.
So the answer is (c) 9 kg.

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