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

A circular race track of radiu 400 m is banked at an angle of 10^(@) . If the coefficient of friction between the wheels of a race car and the road is 0.2, what is the (i) optimum speed of the race car to avoid wear and tear on its tyres? maximum permissible speed to avoid slipping?

A cyclist on a level road takes a sharp circular turn of radius 3 m (g = 10 ms^(-2) ). If the coefficient of static friction between the cycle tyres and the road is 0.2, at which of the following speeds will the cyclist not skid while taking the turn?

A car of mass M moves up an inclined road making an angle theta with the horizontal with constant speed nu . If mu is the coefficient of friction between the tyre of the car and the road, show that the power of the engine of the car is P = nu Mg (sin theta + mu cos theta) .