$A$ car is moving on a circular level road of curvature $300\,m.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr.$

$A$ motorcyclist has to rotate in horizontal circles inside the cylindrical wall of inner radius '$R$' metre. If the coefficient of friction between the wall and the tyres is '$\mu_{s}$',then the minimum speed required is ($g=$ acceleration due to gravity).

$A$ 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? $[g = \text{acceleration due to gravity}]$

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

$A$ plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be

$A$ $0.5 \ kg$ mass is in contact against the inner wall of a cylindrical drum of radius $4 \ m$ rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5 \ rad/s$. The coefficient of friction between the drum's inner wall surface and mass is . . . . . . . (Take $g = 10 \ m/s^2$)