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A grindstone starts revolving from rest. If its angular acceleration is \(4.0\,\text{rad/s}^2\) (uniform), then after 4 s its angular displacement and angular velocity respectively are

1. 32 rad, 16 rad/s
2. 16 rad, 32 rad/s
3. 64 rad, 32 rad/s
4. 32 rad, 64 rad/s

Correct answer: 32 rad, 16 rad/s

Solution

For uniform angular acceleration from rest, \(\omega=\alpha t=4\times 4=16\,\text{rad/s}\). Also, \(\theta=\frac12\alpha t^2=\frac12\times 4\times 16=32\,\text{rad}\). Hence the correct pair is 32 rad, 16 rad/s.

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