A particle moves in a circle of radius $25\,cm$ at two revolutions per sec. The acceleration of the particle in $m/s^2$ is

A single wire $ACB$ passes through a smooth ring at $C$ which revolves at a constant speed in the horizontal circle of radius $r$ as shown in the figure. The speed of revolution is

An aircraft executes a horizontal loop of radius $1.00\; km$ with a steady speed of $900 \;km/h$. Compare its centripetal acceleration with the acceleration due to gravity.

In $1.0\, s$ a particle goes from point $A$ to point $B$, moving in a semicircle of radius $1.0\, m$ (see figure). The magnitude of the average velocity is ......... $m/s$

Figure below shows a body of mass $M$ moving with the uniform speed on a circular path of radius, $R$. What is the change in acceleration in going from ${P_1}$ to ${P_2}$

Two particles, one at the centre of a circle of radius $R$, and another at a point $Q$ on the circle, start moving towards a point $P$ on the circle at the same time (see figure below). Both are at rest initially and move with uniform velocities $\vec{V}_1$ and $\overrightarrow{V_2}$ respectively. They also reach the point $P$ at the same time, If the angle between the velocities is $\theta$ and the angle subtended by $P$ and $Q$ at the centre is $\phi$ (as shown in the figure), then