Sphere "A" has mass m and is moving with velocity "v". It makes a head-on elastic collision with a stationary sphere "B" of; mass 2m. After the collision their speeds (vA and vB are:
Correct answer: C. -v/3, 2v/3
- A. 0, v/2
- B. -v, v
- C. -v/3, 2v/3
- D. -2v/3, v/3
Explanation
In a head-on elastic collision, both momentum and kinetic energy are conserved. The initial momentum is m*v (since sphere B is stationary). After the collision, the momentum must still equal m*v, considering both spheres' movements. The correct equations from these conservation laws result in sphere A having a velocity of -v/3 and sphere B having a velocity of 2v/3. This satisfies m*(-v/3) + 2m*(2v/3) = m*v and conserves kinetic energy as well. The other options fail to maintain both of these conservation principles under the given conditions.
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