JEE Mains · Physics · STD 11 - 4.2 friction

A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if

A \(R \leq \frac{\mu g}{2 \omega^{2}}\)
B \(R \leq \frac{\mu g }{\omega^{2}}\)
C \(R \geq \frac{\mu g}{2 \omega^{2}}\)
D \(R \geq \frac{\mu g }{\omega^{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(R \leq \frac{\mu g }{\omega^{2}}\)

Step-by-step Solution

Detailed explanation

\(f_{s}=m \omega^{2} R\) We know that \(f_{ S } \leq f _{\text {smax }}\) \(m \omega^{2} R \leq \mu m g\) \(R \leq \frac{\mu g }{\omega^{2}}\)

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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