Circular Motion: Centripetal Force Comparison Between Andy and Bella

[dekoi]

Andy and Bella move in circular paths about a common point with the same constant angular velocity $$\omega$$. Bella's mass is half the mass of Andy. The distance, where Andy is from the centre of the circle, is twice the distance of Bella. Who of the two will experience the greater magnitude of the centripetal force, $$F_c$$?

The answer given is that they will experience the SAME force. However, I found otherwise.

Since $$F_c=m\omega^2R$$

$$F_a=m_a\omega^2R_a$$ and $$F_b=m_b\omega^2R_b$$

The ratios I obtained were: $$m_b=\frac{m_a}{2}$$ and $$R_b=\frac{R_a}{2}$$.

When I find the ratio, I get:
$$\frac{F_a}{F_b}=\frac{m_a\omega^2R_a}{m_b\omega^2R_b}=\frac{m_aR_a}{\frac{m_a}{2}\frac{R_a}{2}}$$

My end result will be the value, 4, which is not 1, which I am looking for in order for the forces to be equal.

Is there a problem with my method, or is the answer given the wrong answer?

 

[Doc Al]

I agree with your analysis. The answer is wrong. (Or someone messed up the problem statement.)

 

[dekoi]

Thank you.