પદાર્થને \(h_1\) ઉંચાઈથી જમીન પર છોડવામાં આવે છે અને જમીન પર અથડાયા પછી, તે \(h _2\) ઉંચાઈ સુધી ઉછળે છે. જો જમીન પર અથડાતા પહેલા અને પછી પદાર્થના વેગનો ગુણોત્તર \(4\) હોય, તો પદાર્થની ગતિ ઊર્જામાં પ્રતિશત ત્રુટિ \(\frac{x}{4}\) છે. \(x\) નું મૂલ્ય ...... છે

A \(374\)
B \(373\)
C \(375\)
D \(365\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(375\)

Step-by-step Solution

Detailed explanation

Let \(V_1\) and \(V_2\) are velocity just before and just after hitting the floor. \(\frac{V_1}{V_2}=4 \Rightarrow V_1=4 V_2\) \(K E_{\text {bygove }}=\frac{1}{2} m V_1^2\) \(K E_{\text {affor }}=\frac{1}{2} m V_2^2=\frac{1}{2} \frac{m \cdot V_1^2}{16}\)…

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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