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Question :
51. A solid sphere of mass 4.0 kg and radius : 2102160

51. A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15?. It rolls to the bottom without slipping. The upper end of the ramp is 1.2 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.

A. 70 J

B. 47 J

C. 18 J

D. 8.8 J

52. A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15?, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: *I* = 0.4*MR*^{2} for a solid sphere and *g* = 9.8 m/s^{2})

A. 4.7 m/s

B. 4.1 m/s

C. 3.4 m/s

D. 2.4 m/s

53. A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15?, and rolls to the bottom without slipping. (For a cylinder *I* = 0.5*MR*^{2}) The upper end of the ramp is 1.2 m higher than the lower end. Find the linear speed of the cylinder when it reaches the bottom of the ramp. (*g* = 9.8 m/s^{2})

A. 4.7 m/s

B. 4.3 m/s

C. 4.0 m/s

D. 2.4 m/s

54. A gyroscope has a moment of inertia of 0.14 kg?m^{2} and an initial angular speed of 15 rad/s. Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque?

A. 3.3 ´ 10^{-2} N?m

B. 8.1 ´ 10^{-2} N?m

C. 14 ´ 10^{-2} N?m

D. 7.0 ´ 10^{-2 }N?m

55. A gyroscope has a moment of inertia of 0.140 kg?m^{2 }and has an initial angular speed of 15.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 ´ 10^{-2} N?m, then in what time interval will the gyroscope coast from 15.0 rad/s to zero?

A. 150 s

B. 105 s

C. 90.0 s

D. 180 s