A body revolves with constant speed v in a circular path of radius r. The magnitude of its average acceleration during motion between two points in diametrically opposite direction is 

Two particles $\mathrm{A},\mathrm{ }\mathrm{B}$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega .$ At $t=0,$ their positions and direction of motion are shown in the figure:

The relative velocity $\overrightarrow{V_A}-\overrightarrow{V_B}$ at $t=\frac{\pi }{2\omega }$ is given by:

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.

Two parallel discs are connected by a rigid rod of length $L=0.5 \mathrm{m}$ centrally. Each disc has a slit oppositely placed as shown in the figure. A beam of neutral atoms is incident on one of the discs axially at different velocities $v$, while the system is rotated at angular speed of, $600 \mathrm{rev} {\mathrm{s}}^{-1}$, so that atoms only with a specific velocity emerge at the other end. Calculate the two largest speeds (in meter/second) of the atoms that will emerge at the other end.

A clock has a continuously moving second's hand of $0.1 \mathrm{m}$ length. The average acceleration of the tip of the hand (in units of $\mathrm{m} {\mathrm{s}}^{-2}$) is of the order of :

Two blocks of masses $m$ and $2 \mathrm{m}$ connected by a massless string move along concentric horizontal circles on a horizontal frictionless table with $O$ as fixed point as shown in the figure. If $T$ is the period of motion, the tension in the longer part of the string is (Neglect the dimensions of the blocks when compared with the lengths of the string).