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RE-NEET2026Physics-Circular Motion

RE-NEET 2026 Physics Banked Curves MCQ Question

Type: MCQ-numerical-Medium-Class 11

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 m/s, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 m/s², the value of θ is:

A

tan⁡−1(25)\tan^{-1} \left( \frac{2}{5} \right)

B

tan⁡−1(32)\tan^{-1} \left( \frac{\sqrt{3}}{2} \right)

C

tan⁡−1(23)\tan^{-1} (2 \sqrt{3})

D

tan⁡−1(15)\tan^{-1} \left( \frac{1}{5} \right)

Correct Answer

Option D

Detailed Explanation

To minimize tire wear on a banked curve, the banking angle θ\theta must satisfy the equation derived from the balance of forces:

tan⁡(θ)=v2rg\tan(\theta) = \frac{v^2}{rg}

where vv is the speed of the car, rr is the radius of the track, and gg is the acceleration due to gravity. Substituting the values, we have:

tan⁡(θ)=10250×10=100500=15.\tan(\theta) = \frac{10^2}{50 \times 10} = \frac{100}{500} = \frac{1}{5}.

Thus, θ=tan⁡−1(15)\theta = \tan^{-1} \left( \frac{1}{5} \right), confirming option D as correct.

The other options fail because they do not satisfy the derived relationship for the given speed and radius.

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