Explosion of a Stationary Object – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Collision

Explosion of a Stationary Object

A stationary object explodes into two parts of equal masses, then:
Assertion: Both parts will have same kinetic energy after explosion.
Reason : Both parts will have same momentum after explosion.
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Both Assertion and Reason are true but Reason is not correct explanation of Assertion.
Assertion is true but Reason is false.
Assertion and Reason are false.

Solution:

By conservation of momentum, the two parts move in opposite directions with equal magnitude of momentum, \( \vec{p}_1 = -\vec{p}_2 \). Thus, they have different momenta (since momentum is a vector), so the Reason is false. However, since they have the same mass and same momentum magnitude, their kinetic energy \( K = \frac{p^2}{2m} \) is the same, so the Assertion is true.

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