Rotational Motion Question 150
Question: 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, $\frac{F _{1}}{F _{2}}$ is
Options:
A) ${{\left( \frac{R _{1}}{R _{2}} \right)}^{2}}$
B) $\frac{R _{2}}{R _{1}}$
C) $\frac{R _{1}}{R _{2}}$
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
[c]
$ a _{1}=\frac{v _{1}^{2}}{R _{1}}=\frac{{{\omega }^{2}}R _{1}^{2}}{R _{1}}={{\omega }^{2}}R _{1}~~~$
$a _{2}=\frac{v _{2}^{2}}{R _{2}}={{\omega }^{2}}R _{2}~$
Taking particle masses equal
$\frac{F _{1}}{F _{2}}=\frac{ma _{1}}{ma _{2}}=\frac{a _{1}}{a _{2}}=\frac{R _{1}}{R _{2}}$
