$A$ 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 ........ $km/hr.$

$A$ car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

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 ........ $m/s$.

$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

Two cars are moving on a banked circular path of radius $8 \ m$ having an angle of banking $45^{\circ}$. If the coefficients of static friction between the road and the tyres of the two cars are $0.5$ and $0.4$ respectively,then the ratio of maximum permissible speeds of the cars to avoid slipping is

$A$ 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.