Beginning from a rest position, a solid disk A, a solid ball B, and a hoop C, race down an incline. Rank them in order of finishing: winner, second place, and third place.
To rank:The result of race, down an incline inorder of finishing.
Answer to Problem 20A
The rank of the race, down an incline in an order of finishing is solid ball B, solid disk A, hoop C.
Explanation of Solution
Given:
Solid disk A, a solid ball B and a hoop C are initially at rest. They race down along an inclined plane.
Formula used:
Moment of inertia of rigid body about an axis of rotation is defined as the sum of products of the mass and the square of the distance from the axis of rotation.
The expression for moment of inertia is,
Here,
Calculation:
The expression for moment of inertia of solid disk A is,
Here,
The expression for moment of inertia of solid ball B is,
Here,
The expression for moment of inertia of hoop C is,
Here,
The objects have least moment of inertia produce more speed.
By comparing the values of moment of inertia
Conclusion:
Thus, the rank of the race down an incline in an order of finishing is solid ball B, solid disk A, hoop C.
Chapter 12 Solutions
Conceptual Physics: The High School Physics Program
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