AP EAMCET · PHYSICS · Center of Mass Momentum and Collision

A bullet of mass \(m\) and velocity \(v\) when fired at a sand bag of mass \(M\), suspended by a string, gets embedded into the bag. The loss of kinetic energy in this process is

A \(\frac{m v^2}{2}\)
B \(\frac{m v^2}{2(M+m)}\)
C \(\frac{M v^2}{2}\)
D \(\frac{m M N^2}{2(M+m)}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{m M N^2}{2(M+m)}\)

Step-by-step Solution

Detailed explanation

Mass of the buIlet \(=m\) Speed of bullet \(=v\) According to question, bullets gets embedded into the bag, then they will move with common velocity \(v_1\) (say). This is the case of perfectly enelastic collision. \(\therefore\) Initial kinetic energy of bullet,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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