$A$ 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 $10 \%$,the increase in the radius of curvature will be (Angle of banking and friction is unchanged in both the cases.) (in $m$)

$A$ car is moving on a horizontal curved road with radius $50\,m$. The approximate maximum speed of the car will be $............\,ms^{-1}$,if the coefficient of friction between the tyres and the road is $0.34$. [Take $g = 10\,ms^{-2}$]

Assuming the coefficient of friction between the road and tyres of a car to be $0.5$,the maximum speed with which the car can move round a curve of $40.0\, m$ radius without slipping,if the road is unbanked,should 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?

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

The radius of a curved road is $R$,and the width of the road is $b$. The outer edge of the road is raised by $h$ with respect to the inner edge so that a car with velocity $V$ can pass safely over it. The value of $h$ is ($g =$ acceleration due to gravity).