Write equation of centripetal acceleration and centripetal force for uniform circular motion.

A car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$ . The maximum speed with which the car can move without skidding out is

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

If a cyclist moving with a speed of $4.9\, m/s$ on a level road can take a sharp circular turn of radius $4 \,m$, then coefficient of friction between the cycle tyres and road is

A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if 

A motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between road and tyres is $0.5$, the speed avoiding skidding will be ....... $m/s$