Two cars A and B start racing at the same time on a flat race track which consists of two straight sections each of length 100 \(\pi\) and one circular section as shown in figure. The rule of the race is that each car must travel at constant speed at all times without even skidding :

Car B completes its journey before car A

Maximum velocity for car A : \(v_{A, max} = \sqrt{{\mu_A} {g} {r_A}} = \sqrt{0.1 \times10 \times 100} = 10 \text{ m/s}\)

Maximum velocity for car B : \(v_{B, max} = \sqrt{{\mu_B} {g} {r_B}} = \sqrt{0.2\times 10 \times 200} = 20 \text{ m/s}\)

Time taken by cars and A and B : 

\(t_A = \frac{200 \pi + \pi*100}{100} = 3 \pi  \text{ s ; } t_B = \frac{200 \pi + 200 \pi}{20} = 2 \pi \text{ s}\)