JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Laws of Motion

A coin is placed on a disc. The coefficient of friction between the coin and the disc is

μ

. If the distance of the coin from the center of the disc is

r

, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

(A) $\frac{μg}{r}$
(B) $\frac{r}{μg}$
(C) $\frac{μg}{r}$ ✓ Correct
(D) $\frac{μ}{r g}$

Answer: (C)

Solution

For the coin not to slip, friction must supply the centripetal force:

μ m g \geq m ω^{2} r

The maximum angular velocity occurs when friction is at its limiting value:

μ m g = m ω_{ma x}^{2} r ⟹ ω_{ma x} = \frac{μg}{r}

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Single correct option

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