એક રબર બોલ \(h\) ઉંચાઈથી પડે છે અને \(h / 2\) ઉંચાઈ સુધી રીબાઉન્સ (પાછો ઉછળે) થાય છે. પ્રારંભિક તંત્રની કુલ ઊર્જામાં થતો પ્રતિશત ધટાડો, ઉપરાંત બોલ જમીન ને અથડાય તે પહેલાંનો વેગ અનુક્રમે _______ થશે.

A \(50 \%, \sqrt{\frac{\mathrm{gh}}{2}}\)
B \(50 \%, \sqrt{\mathrm{gh}}\)
C \(40 \%, \sqrt{2 \mathrm{gh}}\)
D \(50 \%, \sqrt{2 \mathrm{gh}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(50 \%, \sqrt{2 \mathrm{gh}}\)

Step-by-step Solution

Detailed explanation

\(\text { Velocity just before collision }=\sqrt{2 \mathrm{gh}}\) \(\text { Velocity just after collision }=\sqrt{2 \mathrm{~g}\left(\frac{\mathrm{h}}{2}\right)}\) \(\therefore \Delta \mathrm{KE}=\frac{1}{2} \mathrm{~m}(2 \mathrm{gh})-\frac{1}{2} \mathrm{mgh}\)…

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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