એક સિક્કાને તક્તી પર ગોઠવેલો છે. આ સિક્કા અને તક્તી વચચે ઘર્ષાણાંક \(\mu\) છે. જ્યારે આ સિક્કાનું તક્તીના કેન્દ્રથી અંતર \(r\) હોય ત્યારે સિકકો તક્તી પર સરકે નહી તે માટે તક્તીને આપી શકાતો મહત્તમ કોણીય વેગ _______ છે.

A \(\frac{\mu g}{r}\)
B \(\sqrt{\frac{\mathrm{r}}{\mu g}}\)
C \(\sqrt{\frac{\mu g}{r}}\)
D \(\frac{\mu}{\sqrt{\mathrm{rg}}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{\frac{\mu g}{r}}\)

Step-by-step Solution

Detailed explanation

\(\mathrm{N}=\mathrm{mg}\) \(\mathrm{f}=\mathrm{m} \omega^2 \mathrm{r}\) \(\mathrm{f}=\mu \mathrm{N}\) \(\mu \mathrm{mg}=\mathrm{mr} \omega^2\) \(\omega=\sqrt{\frac{\mu g}{r}}\)

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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