A wheel rotates so that the angle of rotation is proportional to the square of the time. The first revolution was performed by the wheel for 8 seconds the angular velocity at this time is

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$π rad / \sec$

$2 π rad / \sec$

$\frac{π}{3} rad / \sec$

$\frac{π}{2} rad / \sec$

answer is C.

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Detailed Solution

$θ \propto t^{2} \Rightarrow θ = k t^{2} (k constant)$

$\Rightarrow k = \frac{2 π}{64} \Rightarrow k = \frac{π}{32}$

$\Rightarrow \frac{d θ}{d t} = k \cdot 2 t = \frac{π}{32} \times 2 \times 8 = \frac{π}{2} R / \sec$

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