Thermal Properties of Matter

JEE Main level, single correct, medium

38 of 126

Question 38 of 126

At 40∘C,40^{\circ}C, a brass wire of 1mm1mm radius is hung from the ceiling. A small mass, MM is hung from the free end of the wire. When the wire is cooled down from 40∘C40^{\circ}C to 20∘C20^{\circ}C it regains its original length of 0.2m.0.2m. The value of MM is close to:
(Coefficient of linear expansion and Young’s modulus of brass are
10−5/∘C{10}^{-5}{/}^{^{\circ}}C and 1011N/m2,{10}^{11}N/{m}^{2}, respectively; g=10ms−2g=10m{s}^{-2} )

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Answer: (D) 9kg9kg

Mg=(AYl)ΔlMg=\left(\dfrac{AY}{l}\right)\Delta l
Δll=αΔT\dfrac{\Delta l}{l}=\alpha \Delta T
Mg=(AY)αΔTMg=\left(AY\right)\alpha \Delta T
M=(AY)αΔTg=π×(0.001)2×1011×10−5×2010=2πM=\dfrac{\left(AY\right)\alpha \Delta T}{g}=\dfrac{\pi \times {\left(0.001\right)}^{2}\times {10}^{11}\times {10}^{-5}\times 20}{10}=2\pi
Closest value of
MM is 9 kg.

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