$A$ particle is performing uniform circular motion along the circumference of a circle of diameter $1 \ m$ with a frequency of $4 \ Hz$. The acceleration of the particle in $m/s^2$ is (in $\pi^2$)

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their angular speeds $\omega_{1}$ and $\omega_{2}$ are such that they both complete one revolution in the same time $t$. The ratio of the linear speed of $m_{1}$ to the linear speed of $m_{2}$ is:

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

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

The figure shows a body of mass $m$ moving with a uniform speed $v$ along a circle of radius $r$. The change in velocity in going from $A$ to $B$ is

Motion of a particle in $x-y$ plane is described by a set of following equations $x=4 \sin \left(\frac{\pi}{2}-\omega t\right) \text{ m}$ and $y=4 \sin (\omega t) \text{ m}$. The path of the particle will be: