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)

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) (A) 10 √3 m s-1 (B) 9√10 m s-1 (C) √10 m s-1 (D) 2 √10 m s-1

Tardigrade Admin · Accepted Answer

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 tan θ =√300×10× tan 15° =√810=9√10m s-1

Q. A circular racetrack of radius $300 m$ is banked at an angle of $1 5^{°} .$ 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 $t an 1 5^{\circ} = 0.27, g = 10 m s^{- 2}$ )

$103 m$ $s^{- 1}$

$910 m$ $s^{- 1}$

$10 m$ $s^{- 1}$

$210 m$ $s^{- 1}$

Here, $R = 300 m$ , $θ = 1 5^{\circ}$ , $g = 10 m$ $s^{- 2}$ , $μ = 0.2$
The optimum speed of the car to avoid wear and tear is given by
$v = R g t an θ$
$= 300 \times 10 \times t an 1 5^{\circ}$
$= 810 = 910 m$ $s^{- 1}$

Q. A circular racetrack of radius 300m 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 (Taketan15∘=0.27,g=10ms−2)

103​m s−1

910​m s−1

10​m s−1

210​m s−1