$A$ motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between the road and tyres is $0.5$,the maximum speed to avoid skidding will be ....... $m/s$. (Take $g = 10\,m/s^2$)

$A$ coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table is halved,it will just slip when placed at a distance of $............\,cm$ from the center.

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

$A$ car of mass $m$ moves on a banked road having radius $r$ and banking angle $\theta$. To avoid slipping from the banked road,the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is:

$A$ cyclist moves on a circular track of radius $100 \ m$. If the coefficient of friction is $0.2$,then the maximum velocity with which the cyclist can take the turn while leaning inwards is ...... $m/s$.

$A$ car is moving on a circular path and takes a turn. If $R_1$ and $R_2$ are the reactions on the inner and outer wheels respectively,then: