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

Does the motion of a vehicle on a level circular path depend on the mass of the vehicle?

Which component provides the centripetal force for a vehicle moving at an optimum speed on a banked road?

$A$ railway line is taken round a circular arc of radius $1000 \ m$,and is banked by raising the outer rail $h \ m$ above the inner rail. If the lateral force on the inner rail when a train travels round the curve at $10 \ ms^{-1}$ is equal to the lateral force on the outer rail when the train's speed is $20 \ ms^{-1}$,then the value of $4g \tan \theta$ is equal to: (The distance between the rails is $1.5 \ m$)

Roads are banked on curves so that

The safe speed of a vehicle over a smooth banked road of radius $150\ m$ is $10\ m/s$. If the width of the road is $7.5\ m$,the height of the outer edge is: (in $m$)