$A$ cyclist turns around a curve at $15\, miles/hour$. If he turns at double the speed,the tendency to overturn is

$A$ 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 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 of $800 \,kg$ is taking a turn on a banked road of radius $300 \,m$ and angle of banking $30^{\circ}$. If the coefficient of static friction is $0.2$, then the maximum speed with which the car can negotiate the turn safely is: $(g=10 \,m/s^2, \sqrt{3}=1.73)$ (in $\,m/s$)

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

$A$ disc of radius $5\, m$ is rotating with an angular frequency of $10\, rad/s$. $A$ block of mass $2\, kg$ is to be placed on the disc. If the coefficient of friction between the disc and the block is $\mu_s = 0.4$,find the maximum distance from the axis where the block can be placed without sliding (in $cm$).