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Answer :
The grindstone turns through an angle of 32.00 rad (Option d) during the given time with constant angular acceleration.
The grindstone's angular acceleration is constant, and we know that it increases from 4.00 rad/s to 12.00 rad/s in 4.00 s. We can use the formula:
angular speed = initial angular speed + (angular acceleration x time)
We can rearrange this formula to solve for angular acceleration:
angular acceleration = (angular speed - initial angular speed) / time
Plugging in the values, we get:
angular acceleration = (12.00 rad/s - 4.00 rad/s) / 4.00 s = 2.00 rad/s^2
Now, we can use another formula to find the angle turned:
angle turned = initial angular speed x time + (1/2 x angular acceleration x time^2)
Plugging in the values, we get:
angle turned = 4.00 rad/s x 4.00 s + (1/2 x 2.00 rad/s^2 x (4.00 s)^2) = 32.00 rad
Therefore, the answer is 32.00 rad (Option d).
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