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:

$A$ motorcyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius $8.0 \ m$,with a minimum speed of $5 \sqrt{5} \ m \ s^{-1}$. The minimum value of the coefficient of friction between the tyres and the wall of the well must be (take $g = 10 \ m \ s^{-2}$):

$A$ cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$ through which the cyclist leans inwards is given by

$A$ motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v$. The minimum value of the coefficient of friction so that the negotiation may take place safely is

The radius of a horizontal curved road is $20 \ m$ and the coefficient of friction between the road and the vehicle's tires is $0.25$. What is the safe speed of the vehicle on this road (in $m/s$)? $(g = 9.8 \ m/s^2)$

$A$ 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)