A wheel is subjected to uniform angular acceleration about its ax… - Vidyadip

MCQ

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
$1$
B
$2$
✓
$3$
D
$5$

✓

Answer

Correct option: C.

$3$

c
(c) 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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