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Question

An angular 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, $\frac{F_{1}}{F_{2}}$ is

{(\frac{R_{1}}{R_{2}})}^{2}

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\frac{R_{2}}{R_{1}}

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\frac{R_{1}}{R_{2}}

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Solution

The correct option is C $\frac{R_{1}}{R_{2}}$
$a_{1} = \frac{v_{1}^{2}}{R_{1}} = \frac{ω^{2} R_{1}^{2}}{R_{1}} = ω^{2} R_{1}$
$a_{2} = \frac{v_{2}^{2}}{R_{2}} = ω^{2} R_{2}$
Taking Particle masses equal
$\frac{F_{1}}{F_{2}} = \frac{m a_{1}}{m a_{2}} = \frac{a_{1}}{a_{2}} = \frac{R_{1}}{R_{2}}$

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An angular ring with inner and outer radii R1 and R2 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, F1F2 is

The correct option is C R1R2a1=v21R1=ω2R21R1=ω2R1a2=v22R2=ω2R2Taking Particle masses equal F1F2=ma1ma2=a1a2=R1R2

An angular 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, $\frac{F_{1}}{F_{2}}$ is

The correct option is C $\frac{R_{1}}{R_{2}}$
$a_{1} = \frac{v_{1}^{2}}{R_{1}} = \frac{ω^{2} R_{1}^{2}}{R_{1}} = ω^{2} R_{1}$
$a_{2} = \frac{v_{2}^{2}}{R_{2}} = ω^{2} R_{2}$
Taking Particle masses equal
$\frac{F_{1}}{F_{2}} = \frac{m a_{1}}{m a_{2}} = \frac{a_{1}}{a_{2}} = \frac{R_{1}}{R_{2}}$