JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Rotational Mechanics

The centre of a wheel rolling on a plane surface moves with a speed

v_{0}

. A particle on the rim of the wheel at the same level as the centre will be moving at a speed

x v_{0}

. Then the value of

x

is ______.

Answer: 2

Solution

For rolling without slipping the centre moves with

v_{0} = ω R

. A rim point level with the centre shares the translational velocity

v_{0}

along the surface, and its rotational velocity

ω R = v_{0}

is perpendicular to the radius drawn to it, hence vertical. The two contributions are at right angles, so

v = v_{0}^{2} + v_{0}^{2} = 2 v_{0}

Comparing with

x v_{0}

gives

x = 2

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Integer answer

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