$A$ car of mass $1500 \ kg$ is moving with a speed of $12.5 \ m/s$ on a circular path of radius $20 \ m$ on a level road. What should be the coefficient of friction between the car and the road,so that the car does not slip?

$A$ car when passing through a convex bridge exerts a force on it which is equal to:

The normal reaction $N$ for a vehicle of $800 \, kg$ mass,negotiating a turn on a $30^{\circ}$ banked road at maximum possible speed without skidding is $... \times 10^{3} \, kg \cdot m/s^{2}$. [Given $\cos 30^{\circ} = 0.87, \mu_{s} = 0.2$]

The coefficient of static friction between the road and tyres of a car is $0.4$. The maximum permissible speed of the car is $10 \,ms^{-1}$ on a curved unbanked road. Then the maximum radius of curvature of the road is (acceleration due to gravity $= 10 \,ms^{-2}$)

$A$ child starts running from rest along a circular track of radius $r$ with constant tangential acceleration $a$. After time $t$,the child feels that the shoes have started slipping on the ground. What is the coefficient of friction $\mu$ between the shoes and the ground? $[g = \text{acceleration due to gravity}]$

$A$ car is moving on a horizontal circular track of radius $0.2 \, km$ with a constant speed. If the coefficient of friction between the tyres of the car and the road is $0.45$,then the maximum safe speed of the car is ........ $m/s$. [Take $g = 10 \, m/s^2$]