Question

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 in Fig. The rule of the race is that each car must travel at a constant speed at all times without ever skidding. Then:

• A. Car $A$ completes its journey before car $B$
• B. Both cars complete their journey in same time
• C. Velocity of car $A$ is greater than that of car $B$
• D. Car $B$ completes its journey before car $A$.

Answer 1

Answer: (D)

Car $B$ completes its journey before car $A$.

For cars not to slide

centripetal force$=$ centrifugal force

$\Rightarrow \mu mg=\frac{{mv}^2}{r}\Rightarrow v=\sqrt{\mu rg}$

$A$

$v_A=\sqrt{\frac{1}{10}\times 100\times 10}=10m/s$

Total distance

$=100\pi +2\times 100\pi =300\pi t=\frac{distance}{speed}=\frac{300\pi }{10}$

$=30\pi$sec

$B$

$v_B=\sqrt{\frac{2}{10}\times 200\times 10}=20m/s$

Total distance

$=200\pi +2\times 100\pi =400\pi time=\frac{distance}{speed}=\frac{400\pi }{20\pi }$

$=20\pi$sec

Car $B$ completes its journey before Car $A$.