A stone tied to the end of a string of length $50 \mathrm{cm}$ is whirled in a horizontal circle with a constant speed. If the stone makes $40$ revolutions in $20 \mathrm{s},$ then the speed of the stone along the circle is

A smooth wire is bent into a vertical circle of a radius $a$. A bead $P$ can slide smoothly on the wire. The circle is rotated about the vertical diameter $AB$ as the axis with speed $\omega$ as shown in the figure. The bead $P$ is at rest with respect to the circular ring in the position shown. Then, ${\omega }^2$ is equal to,

A disc of radius $R$ has a light pole fixed perpendicular to the disc at the circumference which in turn has a pendulum of length $R$ attached to its other end as shown in the figure. The disc is rotated with a constant angular velocity $\omega$. The string makes an angle $30°$ with the rod. Then, the angular velocity of the disc is,

A stone of mass $250 \mathrm{g}$ is tied to the end of a string of length $1.0 \mathrm{m}$. It is whirled in a horizontal circle, on a smooth plane, with a frequency of $30 \mathrm{rev} {\min }^{-1}$. The tension developed in the string is .......?