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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
  A wheel is rotating with an angular speed of $20\,rad/sec$. It is stopped to rest by applying a constant torque in $4\ s$. If the moment of inertia of the wheel about its axis is $0.20\ kg-m^2$, then the work done by the torque in two seconds will be .......... $J$
  • A
    $10$
  • B
    $20$
  • ✓
    $30$
  • D
    $40$
✓

Answer

Correct option: C.
$30$
c
${\omega _1} = 20$ $rad/sec$,

${\omega _2} = 0,\,t = 4sec.$

So angular retardation $\alpha  = \frac{{{\omega _1} - {\omega _2}}}{t} = \frac{{20}}{4} = 5\ rad/se{c^2}$

Now angular speed after $2\ sec$,         

${\omega _2} = {\omega _1} - \alpha t$$ = 20 - 5 \times 2$ = $10\,$$rad/sec$

Work done by torque in $2\ sec$ = loss in kinetic energy = $\frac{1}{2}I\,\left( {\omega _1^2 - \omega _2^2} \right)$$ = \frac{1}{2}(0.20)\,({(20)^2} - {(10)^2})$

$ = \frac{1}{2} \times \,\,0.2 \times 300$= $30\ J.$

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