\(m\) દળ ધરાવતું એક કવચ પ્રારંભમાં સ્થિર (વિરામ) સ્થિતિમાં છે. તે \(2: 2: 1\) જેટલા ગુણોત્તરમાં દળ ધરાવતા ત્રણ ટુકડામાં વિસ્ફોટ પામે છે. જો સમાન દળો ધરાવતા ટુકડાઓ એકબીજાથી લંબદિશામાં \(v\) જેટલી ઝડપથી ઉડતા (ગતિ કરતા) હોય,તો ત્રીજા (હલકા) ટુકડાની ઝડપ \(......\) હશે.

A \(\sqrt{2}\,v\)
B \(2 \sqrt{2}\,v\)
C \(3 \sqrt{2}\,v\)
D \(v\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \sqrt{2}\,v\)

Step-by-step Solution

Detailed explanation

By conservation of momentum : \(m(0)=\frac{2 m}{5}(-v \hat{i})+\frac{2 m}{5}(-v \hat{j})+\frac{m}{5} \vec{v}^{\prime}\)

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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