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NEET
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NEET
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Physics
Chapter
Center of Mass, Momentum and Collision

NEET · Physics · Center of Mass, Momentum and Collision

Given below are two statements: one is labelled as Assertion (A)...

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): A projectile moving with velocity vv explodes into two equal fragments. If one fragment is observed to move with velocity 3v3v, the other fragment must be moving with velocity vv.

Reason (R): The velocity of the center of mass of a system remains unchanged during an explosion because the forces of explosion are internal forces.

In the light of the above statements, choose the most appropriate answer from the options given below:

Options

  1. ABoth Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. BBoth Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  3. CAssertion is correct but Reason is incorrect
  4. DAssertion is incorrect but Reason is correct

Correct answer

D. Assertion is incorrect but Reason is correct

Step-by-step solution

Evaluate Assertion (A): By conservation of linear momentum, the total initial momentum equals the total final momentum.

Let the total mass of the projectile be mm.

mv=m2(3v)+m2v2m v = \dfrac{m}{2} (3v) + \dfrac{m}{2} v_2

v=1.5v+0.5v2⇒−0.5v=0.5v2⇒v2=−vv = 1.5v + 0.5 v_2 \Rightarrow -0.5v = 0.5 v_2 \Rightarrow v_2 = -v

The other fragment must move with velocity −v-v, not vv. Thus, the Assertion is incorrect.

Evaluate Reason (R): During an explosion, the forces involved are purely internal. Since there is no net external force acting on the system, the acceleration of the center of mass is zero, and its velocity remains unchanged. Thus, the Reason is correct.

Therefore, Assertion is incorrect but Reason is correct.

Answer: Assertion is incorrect but Reason is correct
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