$A$ car is moving on a circular level road of curvature $300\,m.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr.$

$A$ 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 $\,m$)

$A$ hemispherical bowl of radius $r$ is rotating about its vertical axis of symmetry. $A$ small block kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is $\theta$,then find the angular speed $\omega$ at which the bowl is rotating.

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 $.84$)

The distance between the two tires of a car is $1.5 \, m$. The center of mass of the car is at a height of $2 \, m$ from the ground. To take a turn on a road with a radius of $120 \, m$,the speed of the car should be ........ $m/s$.

$A$ coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$,the maximum angular velocity which can be given to the disc,so that the coin does not slip away,is: