$A$ circular road of radius $1000 \, m$ has a banking angle of $45^\circ$. The maximum safe speed of a car having mass $2000 \, kg$ will be,if the coefficient of friction between the tyre and road is $0.5$,equal to ....... $m/s$.

Two cars are moving on a banked circular path of radius $8 \ m$ having an angle of banking $45^{\circ}$. If the coefficients of static friction between the road and the tyres of the two cars are $0.5$ and $0.4$ respectively,then the ratio of maximum permissible speeds of the cars to avoid slipping is

$A$ body of mass $M \text{ kg}$ is at the top point of a smooth hemisphere of radius $5 \text{ m}$. It is released to slide down the surface of the hemisphere. It leaves the surface when its velocity is $5 \text{ m/s}$. At this instant,the angle made by the radius vector of the body with the vertical is (Acceleration due to gravity $g = 10 \text{ m/s}^2$) (in $^{\circ}$)

$A$ car is crossing a turn at a speed of $10\,m/s$. If the coefficient of friction is $0.5$,then the minimum radius of the turn will be ........ $m$.

$A$ 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

$A$ car turns a corner on a slippery road at a constant speed of $10\,m/s$. If the coefficient of friction is $0.5$,the minimum radius of the arc in meters in which the car turns is: