A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point, such that

Question

A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point, such that, h = R, h = R/3, h = R/2, h = 2R

MARKS App · Accepted Answer

mg cos θ - N = mv 2 R to leave the contact N = 0 mg cos θ = mv 2 R ⇒ g cos θ = v 2 R … 1 cos θ = R - h R … 2 from energy conservation ⇒ 1 2 mv 2 = mgh … 3 from 1, 2, 3 1 2 gR × R - h R = gh ⇒ R - h = 2 h ⇒ h = R / 3

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