In uniform circular motion:
$(i)$ The magnitude of velocity is constant.
$(ii)$ The velocity vector is constant.
$(iii)$ The direction of velocity is constant.
Select the correct statement.

What is the physical quantity represented by the unit $rpm$? Express it in $rad/s$.

For a particle in uniform circular motion,the acceleration $\vec{a}$ at a point $P(R, \theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$-axis):

For a particle executing uniform circular motion:

Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$,respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal acceleration is

An annular ring with inner and outer radii $R_{1}$ and $R_{2}$ is rotating with a uniform angular speed $\omega$ about its central axis. The ratio of the centripetal forces experienced by two particles of equal mass $m$ situated on the inner and outer parts of the ring,$\frac{F_{1}}{F_{2}}$ is