$A$ 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 $m$)

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

On a dry road,the maximum speed of a vehicle along a circular path is $V$. When the road becomes wet,the maximum speed becomes $\frac{V}{2}$. If the coefficient of friction of the dry road is $\mu$,then the coefficient of friction of the wet road 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 negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

$A$ 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)