As seen from above in the image, a string is wrapped around the edge of a uniform cylinder of radius R and mass M which is initially resting motionless on a frictionless table. The end of the string is pulled with a force of F over a distance l. If the linear speed of the cylinder is found to be v after pulling this distance, what is the angular speed of the cylinder? (Note that v ≠ ωR in this case.)

1. ω = √ (4 / MR ^{2}) (Fl - 1/2Mv ^{2})

2. ω = √ (4 / 3MR ^{2}) FR

3. ω = √ (2 / MR ^{2}) (FR - 1/2Mv ^{2})

4. ω = √ (1 / MR ^{2}) Fl

5. ω = √ (2 / 3MR ^{2}) FR

6. ω = √ (4 / MR ^{2}) (FR - 1/2Mv ^{2})

7. ω = √ (2 / MR ^{2}) (Fl - 1/2Mv ^{2})

8. ω = √ (2 / 3MR ^{2}) Fl

9. ω = √ (4 / 3MR ^{2}) Fl

10. ω = √ (1 / MR ^{2}) FR

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