A particle $P$ is moving in a circle of radius $'a'$ with a uniform speed $v$ . $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$ the angular velocity of $P$ about $A$ and $C$ are in the ratio 

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

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega \mathrm{rpm}$. The tension in the string is $T$. If speed becomes $2 \omega$ while keeping the same radius, the tension in the string becomes:

If a force of constant magnitude acts in direction perpendicular to the motion of a particle, then its

If a particle is moving on a circular path with constant speed, then the angle between the direction of acceleration and its position vector w.r.t. centre of circle will be ............ 

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of object is ............