A car is moving on a circular level road of curvature $300\,metres.$ 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 thin circular loop of radius $R$ rotates about its vertical diameter with an angular frequency $\omega .$ Show that a small bead on the wire loop remains at its lowermost point for $\omega \leq \sqrt{g / R} .$ What is the angle made by the radius vector jotning the centre to the bead with the vertical downward direction for $\omega=\sqrt{2 g / R} ?$ Neglect friction.

Do motion of vehicle on level circular path depend on mass of vehicle ?

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $( N )$ and speed of the block $(v)$ ?

If the radius of curvature of the path of two particles of same mass are in the ratio $3:4,$ then in order to have constant centripetal force, their velocities will be in the ratio of:

A body of mass $5\, kg$ is moving in a circle of radius $1\,m$ with an angular velocity of $2$ radian/sec. The centripetal force is ......... $N$