\(0.5\, {kg}\) દળ ધરાવતો પદાર્થ સરળ આવર્ત ગતિ કરે છે. જેનો કંપવિસ્તાર \(5\, {cm}\) અને આવર્તકાળ \((T)\) \(0.2\, {s}\) છે. સમતોલન સ્થાનેથી શરૂ કરીને \(t=\frac{T}{4}\;sec\) સમયે પદાર્થની સ્થિતિઉર્જા (\(J\) માં) કેટલી હશે? દોલનની શરૂઆતની કળા શૂન્ય છે તેમ ધારો.

A \(1.2\)
B \(0.62\)
C \(6.2\)
D \(620\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(0.62\)

Step-by-step Solution

Detailed explanation

by using formula of time period \(T=2 \pi \sqrt{\frac{m}{k}}\) \(0.2=2 \pi \sqrt{\frac{0.5}{k}}\) \(k=50 \pi^{2}\) \(\approx 500\) \(x=A\, \sin (\omega t+\phi)\) \(=5\, c m\, \sin \left(\frac{\omega t}{4}+0\right)\) \(=5\, {cm} \sin \left(\frac{\pi}{2}\right)\) \(=5 \,{cm}\)…

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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