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NEET 2014 (AIPMT) · Rotational Kinematics & Dynamics

Rotational Kinematics & Dynamics question from NEET 2014 (AIPMT)

Q68NEET 2014 · AIPMTMedium

Rotational Kinematics & Dynamics

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions s−2{}^{-2} is

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Answer: (d)

  1. I=12MR2=12(50)(0.5)2=6.25 kg m2I = \frac{1}{2}MR^2 = \frac{1}{2}(50)(0.5)^2 = 6.25\text{ kg m}^2
  2. α=2 rev s−2=4π rad s−2\alpha = 2\text{ rev s}^{-2} = 4\pi\text{ rad s}^{-2}, τ=Iα=25π N m\tau = I\alpha = 25\pi\text{ N m}
  3. T=τR=25π0.5=50π≈157 NT = \frac{\tau}{R} = \frac{25\pi}{0.5} = 50\pi \approx 157\text{ N}
  4. So the answer is (d) 157 N.
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