An unbanked curve has a radius of $60\,m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$,is ........ $m/s$.

$A$ car is driven on a banked road of radius of curvature $20 \ m$ with maximum safe speed. In order to increase its safe speed by $20 \%$,without changing the angle of banking,the increase in the radius of curvature will be (Assume friction is same on the road). (in $m$)

$A$ long horizontal rod has a bead which can slide along its length,and is initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with constant angular acceleration $\alpha$. If the coefficient of friction between the rod and the bead is $\mu$,and gravity is neglected,then the time after which the bead starts slipping is

$A$ stone of mass $1\,kg$ is tied to the end of a massless string of length $1\,m$. If the breaking tension of the string is $400\,N$,then the maximum linear velocity the stone can have without breaking the string,while rotating in a horizontal plane,is $.......\,ms^{-1}$.

For a vehicle moving on a banked curved road,using a free body diagram $(FBD)$,obtain the formula for the maximum safe speed $(v_{max})$.

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 $.84$)