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

$A$ 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 $\,m$)

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

The maximum velocity (in $m/s$) with which a car driver must traverse a flat curve of radius $150 \, m$ and coefficient of friction $0.6$ to avoid skidding is

$A$ disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if