A car travels on a circular racetrack of radius 50 m, which is banked at an angle . If the car travels at a speed 10 ms ⁻¹ , then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be 10 ms ⁻² , the value of is :

Step-by-step solution

For minimum wear and tear on the tyres, the frictional force should be zero. The required centripetal force is provided entirely by the horizontal component of the normal reaction. The optimum speed v on a banked road is given by: v = R g Squaring both sides: v^2 = R g Substituting the given values v = 10 ms ⁻¹ , R = 50 m, and g = 10 ms ⁻² : (10)^2 = 50 10 100 = 500 = 100 500 = 1 5 = ⁻¹ ( 1 5 ) Answer: ⁻¹ ( 1 5 )