A circular racetrack of radius 300 m is banked at an angle of . 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

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 (Take $\tan 15 ° = 0.27, g = 10 {m s}^{- 2}$ )

Smart Achievers · Accepted Answer

(2)

Here, $R = 300 m, θ = 15 °, g = 10 {m s}^{- 2}, μ = 0.2$

The optimum speed of the car to avoid wear and tear is given by

$v = \sqrt{R g \tan θ}$ $= \sqrt{300 \times 10 \times \tan 15 °} = \sqrt{810} = 9 \sqrt{10} {m s}^{- 1}$

Solution

Q.
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 (Take $\tan 15 ° = 0.27, g = 10 {m s}^{- 2}$ )

1 $10 \sqrt{3} {m s}^{- 1}$

2 $9 \sqrt{10} {m s}^{- 1}$

3 $\sqrt{10} {m s}^{- 1}$

4 $2 \sqrt{10} {m s}^{- 1}$

Ans.
(2)

Here, $R = 300 m, θ = 15 °, g = 10 {m s}^{- 2}, μ = 0.2$

The optimum speed of the car to avoid wear and tear is given by

$v = \sqrt{R g \tan θ}$ $= \sqrt{300 \times 10 \times \tan 15 °} = \sqrt{810} = 9 \sqrt{10} {m s}^{- 1}$

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Solution

Q. 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 (Take tan15°=0.27, g=10 m s-2)

1 103 m s-1

2 910 m s-1

3 10 m s-1

4 210 m s-1

Ans. (2) Here, R=300 m, θ=15°, g=10 m s-2, μ=0.2 The optimum speed of the car to avoid wear and tear is given by v=Rg tanθ=300×10×tan15°=810=910 m s-1