Radius relation to centripetal force

[rasen58]

Homework Statement

The radius for the inside of a curve is half the radius for the outside. With 2 cars of equal mass, car A travels on the inside and car B travels on the outside at equal speed. Which statement is correct?
a. The force on A is half the force on B
b. The force on B is half the force on A
c. A 4 times of B
d. B 4 times of A

Homework Equations

Fc = m*v²/R
v = 2piR/T

The Attempt at a Solution

I substituted 2piR/T into v² in the centripetal force equation, and then got
Fc = m*4pi²R/T²
So since the inside radius of half of the outside, the force on A should be half of that on B, which is answer a.
But the answer is apparently b.
But doesn't the equation show that it should be a?

 

[TSny]

In the equation Fc = m*4pi²R/T², what does the symbol T stand for? Does T have the same value for both cars?

Can you see how to answer the question based on Fc = m*v²/R?

 

[rasen58]

T is the period, so I guess the period for B would be twice as long? So then if it is twice as long, then B would indeed be half of A.

Yes, I can see how to answer it with the general centripetal force equation, but I thought that you had to go further.