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A Whee which initially at rest starts rotating at time t = 0. The angular acceleration $α$ decreases from 50 $rad / s^{2}$ to zero value after 5 seconds. During this interval, $α$ varies according to the $α = α_{0} (1 - \frac{t}{5})$ .The angular velocity of the wheel at t = 5 s will be

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125 rad/s

100 rad/s

10 rad/s

250 rad/s

answer is C.

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Detailed Solution

Given $α = α_{0} (1 - \frac{t}{5})$

$α = \frac{dω}{dt} = α_{0} (1 - \frac{t}{5})$

$\int_{0}^{ω} dω = α_{o} \int_{0}^{5} (1 - \frac{t}{5}) dt \Rightarrow ω = α_{0} {[t - \frac{t^{2}}{10}]}_{0}^{5}$

= 50(5- $\frac{25}{10}$ ) rad/s = 125 rad/s

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