A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is
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$5$
A wheel is subjected to uniform angular acceleration about its axis. Initially its angular velocity is zero. In the first $2$ sec, it rotates through an angle ${\theta _1}$. In the next $2$ sec, it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}\over{\theta _1}$ is
Using relation $\theta = {\omega _0}t + \frac{1}{2}a{t^2}$
${\theta _1} = \frac{1}{2}(\alpha ){(2)^2} = 2\alpha $…$(i)$ (As ${\omega _0} = 0,t = 2\,\sec $)
Now using same equation for $t = 4 \,sec$, $\omega_0 = 0$
${\theta _1} + {\theta _2} = \frac{1}{2}\alpha {(4)^2} = 8\alpha $…$(ii)$
From $(i)$ and $(ii)$,
${\theta _1} = 2\alpha $and${\theta _2} = 6\alpha $ $\frac{{{\theta _2}}}{{{\theta _1}}} = 3$
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