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Question #42375
The Question
A solid sphere of mass and radius rolls without slipping down a rough inclined plane that makes an angle with the horizontal. It encounters a sharp concave corner and immediately transitions onto a second inclined plane making an angle with the horizontal. The second inclined plane is completely frictionless. Assuming the collision at the corner is perfectly inelastic in the normal direction (the sphere does not bounce off the second plane), what fraction of the sphere's total kinetic energy is lost during the collision at the corner?
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Variable_Constraint
Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.
Concepts Behind This Question
Moment of Inertia (MOI) Symmetry|Mechanical Energy Conservation|Minimum Force to Move a Block
Why This Question Is Tricky
Common Mistakes
This question tests the precise application of the angular impulse-momentum theorem during a discontinuous transition.
A common trap is assuming that because the object was rolling without slipping, it will continue to do so, or that one must conserve angular momentum about the corner point (as is standard for rough-to-rough transitions).
However, because the second surface is frictionless, the constraint torque vanishes instantaneously.
The only impulse is the normal force from the new incline, which passes through the center of mass.
Consequently, angular velocity is strictly conserved while translational kinetic energy is dissipated, decoupling the rotational and translational kinematics.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | System of Particles and Rotational Motion - Class 11 Part 1 |
| Concept | Moment of Inertia (MOI) Symmetry |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |