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Question

At 40C, 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 40C to 20C 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 105/C and 1011Nm2 respectively; g=10 ms2)

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 kg
Given that, A=πr2=π(103)2

A=π×106 m2

Here, the elongation due to the load and the contraction due to decrease in temperature are the same,

ΔLtemp=ΔLload

LαΔT=FLAY

105×20=Mg(π×106)×1011

Mg=20π

M=2π=6.28 kg

Hence, option (D) is correct.

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