A racing car travel on a track ( without banking) ABCDEFA. ABC is a circular arc of radius 2R.CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The coefficient of friction on the road is $\mu =0.1.$ The maximum speed of the car is 50 $m{s}^{-1}.$ The minimum time for completing one round is 

 

Balancing frictional force for centripetal force, $\frac{m{v}^2}{r}=f=\mu N=\mu mg$

Where, N is normal reaction, $\therefore v=\sqrt{\mu rg}$(where, r is radius of the circular track)

For path ABC, path length $=\frac{3}{4}\left(2\pi 2R\right)=3\pi R=3\pi \times 100=300\pi m$

$v_1=\sqrt{\mu 2Rg}=\sqrt{0.1\times 2\times 100\times 10}=14.14m{s}^{-1}$

$\therefore t_1=\frac{300\pi }{14.14}=66.6s$

For path DEF, Path length $=\frac{1}{4}\left(2\pi R\right)=\frac{\pi \times 100}{2}=50\pi$

$v_2=\sqrt{\mu Rg}=\sqrt{0.1\times 100\times 10}=10m{s}^{-1}$

$t_2=\frac{50\pi }{10}=5\pi s=157s$

For paths CD and FA.
Path length = R + R = 2R = 200 m
$t_3=\frac{200}{50}=4.0s$

$\therefore$Total time for completing one round, $t=t_1+t_2+t_3=66.6+157+4.0=86.3s$