First slide

Dynamics of uniform and non uniform circular motion

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 $π$ and one circular section as in Fig. The rule of the race is that each car must travel at constant speed at all times without ever skidding. The ratio of time taken by car A to car B is

Moderate

Solution

$For max. speed \frac{{mv}_{max}^{2}}{R} = μmg \Rightarrow v_{max} = \sqrt{μgR}$
$\begin{array}{l} v_{A} = \sqrt{0 .1 \times 10 \times 100}, v_{B} = \sqrt{0.2 \times 10 \times 200} \\ = 10 m / \sec, = 20 m / \sec \\ s_{A} = 2 \times 100 π + 100 π = 300 π m, s_{B} = 2 \times 100 π + 200 π = 400 π m, \\ So, t_{A} = 30 π sec. So, t_{B} = 20 πsec \end{array}$

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