PHYSICS · Multi-part · CBSE · Physics · Work and Energy · Work and Energy
Problem
Three identical, solid spheres are each released from rest and allowed to move without friction or air resistance until they reach ground level.
• Sphere X is dropped vertically from a height 3h above the ground.
• Sphere Y rolls smoothly down a frictionless ramp that begins at height 2h and ends at ground level.
• Sphere Z is launched horizontally from the edge of a cliff at height h (its initial horizontal speed is negligible compared with the speed it gains while falling).
Assume the spheres do not spin and can be treated as point particles for energy considerations.
(a) Rank the spheres’ speeds just before they reach the ground from greatest to least. If any are the same, indicate a tie. Clearly justify your ranking using appropriate physical principles rather than numerical calculations.
(b) Rank the spheres’ translational kinetic energies just before impact from greatest to least. Justify your answer qualitatively.
(c) Suppose the mass of Sphere Z were doubled while all other conditions remained the same. Explain qualitatively whether, and how, this change would affect each of your rankings in parts (a) and (b).