The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{\mathrm{v}}=2\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$ and $\overrightarrow{\mathrm{a}}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-2}$, respectively at an instant of time. The radius of the circle is

If the kinetic energy of a particle of mass $m,$ performing uniform circular motion in a circle of radius $r,$ is $E,$ find the acceleration of the particle.

A mass $\text{m}$ moves in a circle on a smooth horizontal plane with velocity ${\mathrm{v}}_0$ at a radius ${\mathrm{R}}_0$ . The mass is attached to a string which passes through a smooth hole in plane as shown.

The tension in the string is increased gradually and finally $\text{m}$ moves in a circle of radius $\frac{{\mathrm{R}}_0}{2}$. The final value of the kinetic energy is:

In the given figure, $a=15 \mathrm{m} {\mathrm{s}}^{-2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of the radius $R=2.5 \mathrm{m}$at a given instant of time. The speed of the particle is