A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8 \mathrm{~m} / \mathrm{s}$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

(A) $4 \sqrt{2} \mathrm{~m} / \mathrm{s}$

(B) $8 \mathrm{~m} / \mathrm{s}$

(C) $4 \mathrm{~m} / \mathrm{s}$

(D) $8 \sqrt{2} \mathrm{~m} / \mathrm{s}$

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Rotational Mechanics

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is

8 m / s

. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

(A) $42 m / s$ ✓ Correct
(B) $8 m / s$
(C) $4 m / s$
(D) $82 m / s$

Answer: (A)

Solution

Rolling without slipping keeps the contact point instantaneously at rest, so the topmost point moves at

2 v_{c m}

; with this equal to

8

m/s the centre moves at

v_{c m} = 4

m/s. At a rim point level with the centre, the translational velocity (horizontal) and the rotational velocity

ω R = v_{c m}

(vertical) are perpendicular and equal in magnitude, so the resultant speed is

v_{c m}^{2} + v_{c m}^{2} = 2 v_{c m} = 42 m/s

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Single correct option

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