A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega _0}$. If the length of the string and angular velocity are doubled, the tension in the string which was initially ${T_0}$ is now

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is

A particle of mass $M$ moves with constant speed along a circular path of radius $ r$ under the action of a force $F$. Its speed is

Write the formula for the maximum permissible speed of a vehicle moving on smooth circular balanced tracks.

A car when passes through a convex bridge exerts a force on it which is equal to

A car of mass $1000\, kg$ negotiates a banked curve of radius $90\, m$ on a frictionless road. If the banking angle is $45^o $, the speed of the car is ....... $ms^{-1}$