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Question :
6. A bucket of water with total mass 23 kg : 2102167

6. A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible, that cylinder turns on frictionless bearings, and that *g* = 9.8 m/s^{2}.)

A. 45 N

B. 68 N

C. 90 N

D. 135 N

7. A uniform bridge span weighs 50.0 ´ 10^{3} N and is 40.0 m long. An automobile weighing 15.0 ´ 10^{3} N is parked with its center of gravity located 12.0 m from the right pier. What upward support force does the left pier provide?

A. 29.5 ´ 10^{3 }N

B. 35.5 ´ 10^{3} N

C. 65.0 ´ 10^{3 }N

D. 32.5 ´ 10^{3} N

8. Masses are distributed in the *x,y*-plane as follows: 6.0 kg at (0.0, 0.0) m, 4.0 kg at (2.0, 0.0) m, and 5.0 kg at (2.0, 3.0) m. What is the *x*-coordinate of the center of gravity of this system of masses?

A. 18 m

B. 2.0 m

C. 1.2 m

D. 1.0 m

9. Masses are distributed in the *xy*-plane as follows: 10 kg at (2.0, 6.0) m, 4.0 kg at (2.0, 0.0) m, and 6.0 kg at (0.0, 3.0) m. Where would a 20-kg mass need to be positioned so that the center of gravity of the resulting four mass system would be at the origin?

A. (1.4, 3.9) m

B. (3.9, 1.4) m

C. (-1.4, -3.9) m

D. (-3.9, -1.4) m

10. A hoop of radius 1.0 m is placed in the first quadrant of an *xy*-coordinate system with its rim touching both the *x*-axis and the *y*-axis. What are the coordinates of its center of gravity?

A. (1.0, 1.0) m

B. (0.7, 0.7) m

C. (0.5, 0.5) m

D. Since there is nothing at the center of the hoop, it has no center of gravity.