$A$ curve on a level road has a radius of $75 \, m$. The maximum speed of a car turning this curved road can be $30 \, m/s$ without skidding. If the radius of the curved road is changed to $48 \, m$ and the coefficient of friction between the tyres and the road remains the same,then the maximum allowed speed would be ......... $m/s$.

$A$ disc revolves with a speed of $33 \frac{1}{3} \; rev/min$,and has a radius of $15 \; cm$. Two coins are placed at $4 \; cm$ and $14 \; cm$ away from the centre of the record. If the coefficient of friction between the coins and the record is $0.15$,which of the coins will revolve with the record?

$A$ 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)

$A$ 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 $.......\,ms^{-1}$.

How is centripetal force provided while taking a turn on a level circular track?

$A$ 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