Question

An angular ring with inner and outer radii R1 and R2 is roling without slipping with a uniform angular speed. The ratio of the force experienced by the two particles situated on the inner and outer parts of the raing, $\frac{F_{1}}{F_{2}}$is:

• A. 1
• B. $\frac{R_{1}}{R_{2}}$
• C. $\frac{R_{2}}{R_{帀}}$
• D. $\left( \frac{R_{1}}{R_{2}} \right)^{2}$

Answer 1

Answer: (B)

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

Answer 2

Let particle A is situated on the inner part and B on the outer part of the ring. As the ring is moving with uniform angular speed therefore both particle will feel centrifugal force

$\frac{F_{1}}{F_{2}} = \frac{F_{A}}{F_{B}} = \frac{m\omega^{2}R_{1}}{m\omega^{2}R_{2}}$⇒ $\frac{F_{1}}{F_{2}} = \frac{R_{1}}{R_{2}}$