A boy on a cycle pedals around a circle of $20\, metres$ radius at a speed of $20\,metres/\sec .$ The combined mass of the boy and the cycle is $90\, kg$. The angle that the cycle makes with the vertical so that it may not fall is ......... $^o$ $(g = 9.8\,m/{\sec ^2})$

Two bodies of equal masses revolve in circular orbits of radii ${R_1}$ and ${R_2}$ with the same period. Their centripetal forces are in the ratio

A car of mass $m$ is moving on a level circular track of radius $R.$ If $\mu_s $ represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by

A stone tied to a string is rotated in a circle. If the string is cut, the stone flies away from the circle because

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