$A$ particle moves on a circular overbridge with constant speed. The friction coefficient varies so that the speed remains constant. Which of the following graphs shows the magnitude of friction $f$ versus the angle $\theta$?

$A$ van is moving with a speed of $108 \,km/hr$ on a level road where the coefficient of friction between the tyres and the road is $0.5$. For the safe driving of the van, the minimum radius of curvature of the road shall be (Acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,m$)

$A$ car of $800 \,kg$ is taking a turn on a banked road of radius $300 \,m$ and angle of banking $30^{\circ}$. If the coefficient of static friction is $0.2$, then the maximum speed with which the car can negotiate the turn safely is: $(g=10 \,m/s^2, \sqrt{3}=1.73)$ (in $\,m/s$)

Assuming the coefficient of friction between the road and tyres of a car to be $0.5$,the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping,if the road is unbanked,should be ......... $m/s$.

The maximum speed of a car on a road-turn of radius $30\, m$,if the coefficient of friction between the tyres and the road is $0.4$,will be .......... $m/s$. (in $.84$)

$A$ car of mass $m$ is moving on a level circular track of radius $R.$ If $\mu_s$ represents the static friction between the road and tyres of the car,the maximum speed of the car in circular motion is given by