A wheel is rotating with uniform angular acceleration covers 50 revolutions in the first five seconds after the start. The angular acceleration of the wheel is

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$3 rev / s^{2}$

$4 rev / s^{2}$

$7 rev / s^{2}$

$2 rev / s^{2}$

answer is C.

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Detailed Solution

$initial angular velocity ω_{1} = 0$

$Angular acceleration = α$

$Time taken t = 5 s$

$Angular displacement θ = 50 rev$

We know

$θ = ω_{1} t + \frac{1}{2} α t^{2}$

$\begin{aligned} \Rightarrow 50 = \frac{1}{2} \times α \times 5^{2} \\ \Rightarrow α = 4 rev / s^{2} \end{aligned}$

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