$A$ particle is moving along a circle such that it completes one revolution in $40 \, s$. In $2 \, \text{minutes} \, 20 \, s$, the ratio $\frac{|\text{displacement}|}{\text{distance}}$ is:

$A$ body moves along a circular path of diameter $30 \text{ cm}$. It starts from one end of a diameter, moves along the circular path, and reaches the other end of the diameter in $3 \text{ seconds}$. The angular speed of the body in radians per second is:

Centripetal acceleration of a cyclist completing $7$ rounds in a minute along a circular track of radius $5 \, m$ with a constant speed,is ......... $m/s^2$.

$A$ particle moves in the $x-y$ plane according to the rules $x = a \sin \omega t$ and $y = a \cos \omega t$. The particle follows:

An object moves at a constant speed along a circular path in the horizontal $XY$ plane with the center at the origin. When the object is at $x = -2 \, m$,its velocity is $-(4 \, m/s) \hat{j}$. What is the object's acceleration when it is at $y = 2 \, m$?

$A$ particle is moving in $U.C.M.$ with speed $V$ and radius $R$. The angular acceleration of the particle is