$A$ motor car has a width of $1.1 \ m$ between its wheels. Its center of gravity is $0.62 \ m$ above the ground and the coefficient of friction between the wheels and the road is $0.8$. What is the maximum possible speed in $m/s$ if the center of gravity moves in a circle of radius $15 \ m$ on a horizontal road surface?

$A$ small mass $m$ rests at the edge of a horizontal disc of radius $R$. The coefficient of static friction between the mass and the disc is $\mu$. The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $h$ meters below. What was its horizontal distance of travel from the point it left the disc?

$A$ cyclist speeding at $18 \; km/h$ on a level road takes a sharp circular turn of radius $3 \; m$ without reducing the speed. The coefficient of static friction between the tyres and the road is $0.1$. Will the cyclist slip while taking the turn?

On which road do we get maximum speed: a circular road with a slope (banked road) or a level circular road?

$A$ circular road of radius $1000 \, m$ has a banking angle of $45^\circ$. The maximum safe speed of a car having mass $2000 \, kg$ will be,if the coefficient of friction between the tyre and road is $0.5$,equal to ....... $m/s$.

$A$ modern grand-prix racing car of mass $m$ is travelling on a flat track in a circular arc of radius $R$ with a speed $v$. If the coefficient of static friction between the tyres and the track is $\mu_{s},$ then the magnitude of negative lift $F_{L}$ acting downwards on the car is (Assume forces on the four tyres are identical and $g =$ acceleration due to gravity)