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Question

# At 40∘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 40∘C to 20∘C 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/∘C and 1011Nm−2 respectively; g=10 ms−2)

A
0.5 kg
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B
6.3 kg
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C
9 kg
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D
1.5 kg
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Solution

## The correct option is B 6.3 kgGiven that, A=πr2=π(10−3)2 A=π×10−6 m2 Here, the elongation due to the load and the contraction due to decrease in temperature are the same, ΔLtemp=ΔLload LαΔT=FLAY ⇒10−5×20=Mg(π×10−6)×1011 ⇒ Mg=20π ⇒M=2π=6.28 kg Hence, option (D) is correct.

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