JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Laws of Motion

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A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of ______ from the centre:

(A)2 cm
(B)1 cm
(C)8 cm
(D)4 cm✓ Correct

Answer: (D)

Solution

On the verge of slipping the limiting friction supplies the centripetal force,

μ m g = m ω^{2} r

, so

r = \frac{μg}{ω ^{2}}

and

r \propto \frac{1}{ω ^{2}}

. Halving the angular velocity multiplies the radius by

4

, so the coin just slips at

4 \times 1 = 4

cm from the centre.

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Single correct option

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