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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 initially at rest, is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in first one second and through an additional angle ${\theta _2}$ in the next one second. The ratio $\frac{{{\theta _2}}}{{{\theta _1}}}$ is
  • A
    $4$
  • B
    $2$
  • ✓
    $3$
  • D
    $1$
✓

Answer

Correct option: C.
$3$
c
Angular displacement in first one second ${\theta _1} = \frac{1}{2}\alpha \,{(1)^2} = \frac{\alpha }{2}$  ......$(i)$      [From $\theta  = {\omega _1}t + \frac{1}{2}\alpha \,{t^2}$]

Now again we will consider motion from the rest and angular displacement in total two seconds

${\theta _1} + {\theta _2} = \frac{1}{2}\alpha \,{(2)^2} = 2\alpha $                                   ......$(ii)$

Solving $(i)$ and $(ii)$, we get ${\theta _1} = \frac{\alpha }{2}$ and ${\theta _2} = \frac{{3\alpha }}{2}$    $\therefore $  $\frac{{{\theta _2}}}{{{\theta _1}}} = 3$.

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