Circular MotionMedium
Question
A car travels on a circular racetrack of radius 50 m , which is banked at an angle $\theta$. If the car travels at a speed $10{\text{ }ms}^{- 1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10{\text{ }ms}^{- 2}$, the value of $\theta$ is:
Options
A.$\tan^{- 1}(\sqrt{3}/2)$
B.$\tan^{- 1}(2\sqrt{3})$
C.$\tan^{- 1}\left( \frac{1}{5} \right)$
D.$\tan^{- 1}\left( \frac{2}{5} \right)$
Solution
Sol. [Key Concept: Banked road — v = √(rg tanθ)]
$tan\theta = \frac{v^{2}}{rg} = \frac{10 \times 10}{50 \times 10} = \frac{1}{5}$
$$\theta = \tan^{- 1}\left( \frac{1}{5} \right)$$
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