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MHT CET 2021 (23 Sep, Shift 1) · Rotational Kinetic Energy, Work & Power

Rotational Kinetic Energy, Work & Power question from MHT CET 2021 (23 Sep, Shift 1)

Q34MHT CET 2021 · 23 SEP · SHIFT 1Medium

Rotational Kinetic Energy, Work & Power

A molecule consists of two atoms each of mass 'mm' and separated by a distance 'dd'. At room temperature, if the average rotational kinetic energy is 'EE' then the angular frequency is

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Answer: (a)

  1. Axis through the centre, each atom at d2\frac{d}{2}: I=2m(d2)2=md22I = 2m\left(\frac{d}{2}\right)^2 = \frac{md^2}{2}
  2. E=12Iω2=md2ω24E = \frac{1}{2}I\omega^2 = \frac{md^2\omega^2}{4}
  3. ω=2dEm\omega = \frac{2}{d}\sqrt{\frac{E}{m}}
  4. So the answer is (a) 2dEm\frac{2}{d}\sqrt{\frac{E}{m}}.
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