JEE Main · 2005 · 08 May 2005 · Offline · Rotational Mechanics

An annular ring with inner and outer radii

R_{1}

and

R_{2}

is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring,

F_{1} / F_{2}

(A) $\frac{R _{2}}{R _{1}}$
(B) $(\frac{R _{1}}{R _{2}})^{2}$
(C)1
(D) $\frac{R _{1}}{R _{2}}$ ✓ Correct

Answer: (D)

Solution

Both particles sit on the same rolling ring and turn with the same angular speed

ω

, so each needs a centripetal force

F = m ω^{2} r

directed towards the axis. For the inner particle

F_{1} = m ω^{2} R_{1}

and for the outer one

F_{2} = m ω^{2} R_{2}

, with equal masses and the same

ω

. Dividing,

\frac{F _{1}}{F _{2}} = \frac{R _{1}}{R _{2}}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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