The optimum speed of the race car to avoid wear and tear on its tyres is, the maximum permissible speed to avoid slipping is

Question

A circular racetrack of radius 300 m is banked at an angle of $15 °$ . The coefficient of friction between the wheels of a race car and the road is 0.2. The optimum speed of the race car to avoid wear and tear on its tyres is, the maximum permissible speed to avoid slipping is (Take $\tan 15 ° = 0.27, g = 10 {m s}^{- 2}$ )

Smart Achievers · Accepted Answer

(3)

The maximum permissible speed is given by

$\tan 15 ° = 0.27, g = 10 {m s}^{- 2}$ $= \sqrt{\frac{300 \times 10 \times (0.2 + 0.27)}{1 - 0.2 \times 0.27}} = 38.6 {m s}^{- 1}$

Solution

1 18.6 $m s^{- 1}$

2 28.6 $m s^{- 1}$

3 38.6 $m s^{- 1}$

4 48.6 $m s^{- 1}$

Ans.
(3)

The maximum permissible speed is given by

$v_{\max} = \sqrt{\frac{R g (μ + \tan θ)}{1 - μ \tan θ}}$ $= \sqrt{\frac{300 \times 10 \times (0.2 + 0.27)}{1 - 0.2 \times 0.27}} = 38.6 {m s}^{- 1}$

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Solution

1 18.6 m s-1

2 28.6 m s-1

3 38.6 m s-1

4 48.6 m s-1