$A$ car is moving with speed $v$ on a banked road of radius $50 \ m$,width $10 \ m$,and height $1.5 \ m$. The velocity $v$ of the car is ......... $m/s$.

$A$ horizontal curve on a racing track is banked at a $45^o$ angle. When a vehicle goes around this curve at the curve's safe speed (no friction needed to stay on the track),what is its centripetal acceleration?

On a railway curve,the outside rail is laid higher than the inside one so that the resultant force exerted on the wheels of the rail car by the tops of the rails will:

$A$ 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:

$A$ car of mass $1000\,kg$ negotiates a banked curve of radius $90\,m$ on a frictionless road. If the banking angle is $45^\circ$,the maximum speed of the car is ............ $m/s$ $[g = 10\,m/s^2]$.

$A$ circular freeway entrance and exit are commonly banked to control a moving car at $14 \ m/s$. To design a similar ramp for $28 \ m/s$, one should: