A cyclist riding the bicycle at a speed of $14 \sqrt{3} \,m / s$ takes a turn around a circular road of radius $20 \sqrt{3} \,m$ without skidding. What is his inclination to the vertical?

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 ......... $N$

A train runs along an unbanked circular track of radius $30 \;m$ at a speed of $54\; km / h$ The mass of the train is $10^{6}\; kg$. What provides the centripetal force required for this purpose - The engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

A block of mass $m$ is kept on horizontal turn table at $x$ distance from the centre. If coefficient of friction between block and surface of turn table is $\mu$, then maximum angular speed of the table so that block does not slip

A car is moving on a horizontal curved road with radius $50\,m$. The approximate maximum speed of car will be $............\,ms^{-1}$, if friction between tyres and road is $0.34.\left[\right.$ Take $\left.g =10 ms ^{-2}\right]$

A cyclist is travelling with velocity $v$ on a curved road of radius $R$. The angle $\theta$  through which the cyclist leans inwards is given by