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 $.84$)

$A$ 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 $g = 10\,ms^{-2}$]

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

$A$ cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed,the tendency to overturn is

$A$ disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. $A$ coin placed at a distance of $1.25\,cm$ from the axis of rotation remains at rest on the disc. Find the coefficient of friction between the coin and the disc. (Take $g = 10\,m/s^2$)

$A$ 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 $m$)