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JEE Main 201912 AprilMorning Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Morning Shift
Subject
Physics
Chapter
Thermal Properties of Matter

JEE Main 2019 · 12 April · Morning Shift · Physics · Thermal Properties of Matter

At 40 ° C, a brass wire of 1mm radius is hung from the ceiling. A...

At 40°C,40 ° 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 ° C to 20°C20 ° 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}{/}^{°}C and 1011N/m2,{10}^{11}N / {m}^{2}, respectively; g=10ms−2g = 10m{s}^{- 2} )

Options

  1. A0.9kg0.9kg
  2. B0.5kg0.5kg
  3. C1.5kg1.5kg
  4. D9kg9kg

Correct answer

D. 9kg9kg

Step-by-step solution

Mg=(AYl)\DeltalMg = \left(\dfrac{AY}{l}\right)\Deltal
\Deltall=α\DeltaT\dfrac{\Deltal}{l} = \alpha\DeltaT
Mg=(AY)α\DeltaTMg = \left(AY\right)\alpha\DeltaT
M=(AY)α\DeltaTg=π×(0.001)2×1011×10−5×2010=2πM = \dfrac{\left(AY\right)\alpha\DeltaT}{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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