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(C) Given that the wheel starts from rest,the initial angular velocity ${\omega _0} = 0$. Let the uniform angular acceleration be $\alpha$.Using the k

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$3$

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(C) Given that the wheel starts from rest,the initial angular velocity ${\omega _0} = 0$. Let the uniform angular acceleration be $\alpha$.Using the kinematic equation for angular displacement: $	heta = {\omega _0}t + \frac{1}{2}\alpha {t^2}$.For the first $1 \ s$ $(t = 1 \ s)$: ${	heta _1} = 0(1) + \frac{1}{2}\alpha {(1)^2} = \frac{\alpha }{2}$ ......$(i)$.For the total time of $2 \ s$ $(t = 2 \ s)$: The total angular displacement is ${	heta _{total}} = {	heta _1} + {	heta _2}$.${	heta _1} + {	heta _2} = 0(2) + \frac{1}{2}\alpha {(2)^2} = 2\alpha$ ......$(ii)$.Subtracting equation $(i)$ from equation $(ii)$ to find ${	heta _2}$:${	heta _2} = 2\alpha - \frac{\alpha }{2} = \frac{{3\alpha }}{2}$.Now,calculating the ratio $\frac{{{	heta _2}}}{{{	heta _1}}}$:$\frac{{{	heta _2}}}{{{	heta _1}}} = \frac{{3\alpha / 2}}{{\alpha / 2}} = 3$.

$A$ wheel,initially at rest,is rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta _1}$ in the first $1 \ s$ and through an additional angle ${\theta _2}$ in the next $1 \ s$. The ratio $\frac{{\theta _2}}{{\theta _1}}$ is

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