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NEET 2019
Exam
NEET
Year
2019
Subject
Physics
Chapter
Rotational Motion

NEET 2019 · Physics · Rotational Motion

A solid cylinder of mass 2kg and radius 4cm is rotating about its...

A solid cylinder of mass 2kg2kg and radius 4cm4cm is rotating about its axis at the rate of 3rpm3rpm. The torque required to stop after 2π2\pi revolutions is

Options

  1. A2×10−6Nm2 \times {10}^{- 6}Nm
  2. B2×10−3Nm2 \times {10}^{- 3}Nm
  3. C12×10−4Nm12 \times {10}^{- 4}Nm
  4. D2×106Nm2 \times {10}^{6}Nm

Correct answer

A. 2×10−6Nm2 \times {10}^{- 6}Nm

Step-by-step solution

From rotational kinematic equations,
ωf2−ωi2=2α\theta{\omega}_{f}^{2} - {\omega}_{i}^{2} = 2\alpha\text{\theta}
02−(32π60)2=2α2π(2π){0}^{2} - {\left(3\dfrac{2\pi}{60}\right)}^{2} = 2\alpha2\pi\left(2\pi\right)
α=−1800rads−2\alpha = - \dfrac{1}{800}rad{s}^{- 2}
∴∴ Torque required τ=∣Iα∣τ = \left|I\alpha\right|
=2(4×10−2)22×1800= \dfrac{2{\left(4 \times {10}^{- 2}\right)}^{2}}{2} \times \dfrac{1}{800}
=16×10−4800= \dfrac{16 \times {10}^{- 4}}{800}
=2×10−6Nm= 2 \times {10}^{- 6}Nm
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