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Physics Question on Motion in a plane

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≤μg2ω2R≤\frac{μg}{2ω^2}

B

R≤μgω2R≤\frac{μg}{ω^2}

C

R≥μg2ω2R≥\frac{μg}{2ω^2}

D

R≥μgω2R≥\frac{μg}{ω^2}

Answer

R≤μg2ω2R≤\frac{μg}{2ω^2}

Explanation

Solution

The correct option is(B): R≤μgω2R≤\frac{μg}{ω^2}

To move together

ω2 R ≤ μ g

R≤μgω2R≤\frac{μg}{ω^2}