TS EAMCET · Physics · Laws of Motion
A circular path of radius 75 m is banked at an angle of \(\tan ^{-1}(0.2)\). If the coefficient of static friction between the tyres of the car and the circular path is 0.1, then the maximum permissible speed of the car to avoid slipping is
- A \(10 \mathrm{~ms}^{-1}\)
- B \(20 \mathrm{~ms}^{-1}\)
- C \(15 \mathrm{~ms}^{-1}\)
- D \(30 \mathrm{~ms}^{-1}\)
Answer & Solution
Correct Answer
(C) \(15 \mathrm{~ms}^{-1}\)
Step-by-step Solution
Detailed explanation
\(v_{max} = \sqrt{rg \frac{\tan\theta + \mu_s}{1 - \mu_s \tan\theta}}\) \(v_{max} = \sqrt{75 \times 9.8 \frac{0.2 + 0.1}{1 - 0.1 \times 0.2}}\) \(v_{max} = \sqrt{75 \times 9.8 \frac{0.3}{0.98}} = \sqrt{225}\) \(v_{max} = 15 \mathrm{~ms}^{-1}\)
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