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Three rolling objects are moving at the same speed on a level surface. The objects are all solid spheres: sphere A has radius r and mass m, sphere B has radius 2r and mass m; sphere C has radius r and mass 2m.The three objects then roll up an incline. Assuming each rolls without slipping, which will (a) roll to the highest vertical point (as measured by the change in the location of the center of mass)? (A) Sphere A (B) Sphere B (C) Sphere C (D) They will all roll to the same height. (b) roll the farthest distance as measured along the incline? (A) Sphere A (B) Sphere B (C) Sphere C (D) They will all roll the same distance.

Three rolling objects are moving at the same speed on a level surface. The objects are all solid spheres: sphere A has radius r and mass m, sphere B has radius 2r and mass m; sphere C has radius r and mass 2m.The three objects then roll up an incline. Assuming each rolls without slipping, which will
(a) roll to the highest vertical point (as measured by the change in the location of the center of mass)?
(A) Sphere A (B) Sphere B (C) Sphere C (D) They will all roll to the same height.
(b) roll the farthest distance as measured along the incline? (A) Sphere A (B) Sphere B (C) Sphere C
(D) They will all roll the same distance.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
(a) The correct option is (B) sphere B.
Acceleration a of a body rolling down an inclined plane will be,
234-2157_1.JPG
Here g is the free fall acceleration, K is the radius of gyration, θ is the angle of inclination with horizontal and R is the radius of the body.
The above equation signifies that, the object which has radius more, the more will be the acceleration of that object and the acceleration of the object does not depend upon the mass of the object M. As the radius of sphere B is more than the sphere A and C, therefore the acceleration of sphere B will be more than A and C. Thus sphere B roll to the highest vertical point. From the above observation we conclude that, option (B) is correct.
(b)
The correct option is (B) sphere B.
The object which has greater acceleration greater will be roll to the highest vertical point. Thus this object will roll the farthest distance as measured along the incline. As the sphere B roll to the highest vertical point, therefore sphere B will roll to the farthest distance as measured along the incline. From the above observation we conclude that, option (B) is correct.

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