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JEE Main 2020 (2 Sep, Shift 2) · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from JEE Main 2020 (2 Sep, Shift 2)

Q54JEE Main 2020 · 2 SEP · SHIFT 2Medium

Angular Momentum & its Conservation

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0.1 kg-m2 and 10 rad s–1 respectively while those for the second one are 0.2 kg-m2 and 5 rad s–1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is:

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Answer: (a)

  1. Total L=0.1(10)+0.2(5)=2 kg m2/sL = 0.1(10) + 0.2(5) = 2\ \text{kg m}^2\text{/s}, total I=0.3 kg m2I = 0.3\ \text{kg m}^2.
  2. ω=20.3=203 rad/s\omega = \frac{2}{0.3} = \frac{20}{3}\ \text{rad/s}
  3. K=L22I=40.6=203 JK = \frac{L^2}{2I} = \frac{4}{0.6} = \frac{20}{3}\ \text{J}
  4. So the answer is (a) 203\frac{20}{3} J.
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