If the speed $(v)$ and radius $(r)$ of a particle performing uniform circular motion are both doubled,find its new centripetal acceleration.

$A$ particle moves such that its position vector $\overrightarrow{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}$,where $\omega$ is a constant and $t$ is time. Which of the following statements is true for the velocity $\overrightarrow{v}(t)$ and acceleration $\overrightarrow{a}(t)$ of the particle?

If a particle moves in a circle describing equal angles in equal times,its velocity vector

$A$ particle is moving on a circular path with a constant speed $v$. Its change of velocity as it moves from $A$ to $B$ in the figure is

Two bodies of equal masses revolve in circular orbits of radii $R_1$ and $R_2$ with the same period. Their centripetal forces are in the ratio:

As shown in the figure,a particle is moving with a constant speed $v = \pi \, m/s$ in a circular path. Considering its motion from point $A$ to point $B$,where the angle subtended at the center is $120^{\circ}$,the magnitude of the average velocity is: