\(m\) દળનો એક પ્રોટોન બીજા અજ્ઞાત દળવાળા કોઈ સ્થિર કણ સાથે સ્થિતિત્સ્થાપક સંઘાત પામે છે. સંઘાત બાદ, પ્રોટોન અને અજ્ઞાત કણ એકબીજા ની સાપેક્ષે \(90^o\) ના ખૂણે ગતિ કરે છે. તો અજ્ઞાત કણનું દળ શું થશે?

A \(\frac{m}{{\sqrt 3 }}\)
B \(\frac{m}{2}\)
C \(2m\)
D \(m\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(m\)

Step-by-step Solution

Detailed explanation

Apply principle of conservation of momentum along \(x-direction,\) \(mu=mv_1\) \(\cos {45^ \circ } + M{v_2}\cos {45^ \circ }\) \(mu = \frac{1}{{\sqrt 2 }}\left( {m{v_1} + M{v_2}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\) Along \(y-direction,\)…

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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