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 ω. The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ. The beaker will revolve with the disc if: (a) R ≤ (μ g)/(2ω²) (b) R ≤ (μ g)/(ω²) (c) R ≥ (μ g)/(2ω²) (d) R ≥ (μ g)/(ω²)

Answer: (b). Friction must supply the centripetal force: mω² R ≤ μ m g. R ≤ (μ g)/(ω²) So the answer is (b).

A disc with a flat small bottom beaker placed on it at a distance R… | JEE Main 2022 (25 Jun, Shift 2)

Q9JEE Main 2022 · 25 JUN · SHIFT 2Easy

Level Road & Rotating Platform

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:

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Answer: (b)

Friction must supply the centripetal force: $m\omega^2 R \le \mu m g$ .
$R \le \frac{\mu g}{\omega^2}$
So the answer is (b).

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