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NEET 2013 · Angular Momentum & its Conservation

Angular Momentum & its Conservation question from NEET 2013

Q78NEET 2013Medium

Angular Momentum & its Conservation

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D1 has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s−1{}^{-1}. Disc D2 has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s−1{}^{-1}. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s−1{}^{-1}) of the system is

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Answer: (b)

  1. I1=12(2)(0.2)2=0.04 kg m2I_1 = \frac{1}{2}(2)(0.2)^2 = 0.04\ \text{kg m}^2, I2=12(4)(0.1)2=0.02 kg m2I_2 = \frac{1}{2}(4)(0.1)^2 = 0.02\ \text{kg m}^2.
  2. Conservation of LL: I1ω1+I2ω2=(I1+I2)ωI_1\omega_1 + I_2\omega_2 = (I_1+I_2)\omega.
  3. ω=0.04(50)+0.02(200)0.06=60.06=100 rad s−1\omega = \frac{0.04(50) + 0.02(200)}{0.06} = \frac{6}{0.06} = 100\ \text{rad s}^{-1}
  4. So the answer is (b) 100.
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