A car travels on a circular racetrack of radius 50 m, which is banked at an angle θ. If the car travels at a speed 10 ms⁻¹, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 ms⁻², the value of θ is: (a) tan ⁻¹(2√(3)) (b) tan ⁻¹(1/5) (c) tan ⁻¹(2/5) (d) tan ⁻¹(√(3)/2)

Answer: (b). Tyre wear is minimum when no friction is needed: tan θ = v²/rg. tan θ = (10²)/(50 × 10) = 1/5 So the answer is (b) θ = tan ⁻¹(1/5).

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Circular Motion (Related PYQs)

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:

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Answer: (b)

Tyre wear is minimum when no friction is needed: $\tan\theta = \frac{v^2}{rg}$ .
$\tan\theta = \frac{10^2}{50 \times 10} = \frac{1}{5}$
So the answer is (b) $\theta = \tan^{-1}\left(\frac{1}{5}\right)$ .

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