The maximum tension which an inextensible ring of mass $0.1\, kg/m$ can bear is $10\,N$. The maximum velocity in $m/s$ with which it can be rotated is ........ $m/s.$

$A$ bike moving at a speed of $60 \; km/hr$ takes a turn with a radius of $0.1 \; km$. At what angle with the vertical should the bike be tilted to avoid slipping?

$A$ particle describes a horizontal circle on the smooth inner surface of a cone as shown in the figure. If the height of the circle above the vertex is $10 \ cm$,find the speed of the particle. (Given: acceleration due to gravity $g = 10 \ m/s^2$ and assume the semi-vertical angle $\theta = 45^\circ$ based on the geometry of the cone). (in $m/s$)

$A$ 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?

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 maximum speed that can be achieved without skidding by a car on a circular unbanked road of radius $R$ and coefficient of static friction $\mu$ is