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Assertion: A sphere of mass $m$ moving with speed $u$ undergoes a perfectly elastic head-on collision with another sphere of heavier mass $M$ at rest $(M>m)$. Then the direction of velocity of the sphere of mass $m$ is reversed after the collision (no external force acts on the system of the two spheres). Reason: During a collision of spheres of unequal masses, the heavier mass exerts more force on the lighter mass than the force which the lighter mass exerts on the heavier mass.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If Assertion is true but reason is false.
4. If both assertion and reason are false.

Correct answer: If Assertion is true but reason is false.

Solution

For a perfectly elastic head-on collision with a heavier target at rest, the lighter sphere can rebound, so the assertion is true. However, by Newton’s third law, the forces exerted by the two spheres on each other are always equal in magnitude and opposite in direction, so the reason is false.

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