(a) Take into account that the centrifugal force experienced by each car is given by:
[tex]\begin{gathered} F_1=m\frac{v^2_1}{R_1} \\ F_2=m\frac{v^2_2}{R_2} \end{gathered}[/tex]
where v1 and v2 are the speed of both cars and R1 and R2 are the radius of the curve traveled by each car, m is the mass of the cars.
If you solve for m, you obtain:
[tex]\begin{gathered} m=\frac{F_1R_1}{v^2_1} \\ m=\frac{F_2R_2}{v^2_2} \end{gathered}[/tex]
due to the masses of the cars are identical, you have:
[tex]\frac{F_1R_1}{v^2_1}=\frac{F_2R_2}{v^2_2}[/tex]
(b) Now, consider that:
R1 = 2R
v1 = v
R2 = 6R
v2 = 3v
Now, divide the equation for F1 over the equation for F2, replace the previous expressions for the parameters and simplify for F1:
[tex]\begin{gathered} \frac{F_1_{}}{F_2}=\frac{m\frac{v^2_1}{R_1}}{m\frac{v^2_2}{R_2}} \\ \frac{F_1_{}}{F_2}=\frac{v^2_1R_2}{v^2_2R_1}=\frac{v^2\cdot6R}{(3v)^2\cdot2R} \\ \frac{F_1}{F_2}=\frac{1}{3} \\ F_1=\frac{1}{3}F_2 \end{gathered}[/tex]
