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A pulley of radius 2 m is rotated about its axis by a force F=(20t-5t^(2)) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotationis 10kgm^(2), the number of rotations made by the pulley before its direction of motion is reversed, is : |
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Answer» more than 3 but less than 6 `tau=Ialpha=Fror10xxalpha=(20t-5t^(2))xx2` or `alpha=4t-t^(2) and omega=(d theta)/(dt)` Also `(d theta)/(dt)=alpha.t` or `d theta=alpha.TDT` `d theta(4t-t^(2)).tdt=(4t^(2)-t^(3))dt` Integrating both SIDES `theta=(4t^(3))/(3)-(t^(4))/(4)` If n rotations are completed in 4s, then putting `t=4` `therefore theta=2pin=(4xx64)/(3)-64=(64)/(3)~=3.4` But `3lt3.4lt6` |
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