Three point particles $P, Q, R$ move in circle of radius $‘r’$ with different but constant speeds. They start moving at $t = 0$ from their initial positions as shown in the figure. The angular velocities (in rad/ sec) of $P, Q$ and $R$ are $5\pi , 2\pi$ & $3\pi$ respectively, in the same sense.  the number of times $P$ and $Q$ meet in that time interval is:

A particle is moving on a circular path with constant speed $v$. It moves between two points $A$ and $B$. which subtends an angle $60^{\circ}$ at the centre of circle. The magnitude of change in its velocity and change in magnitude of its velocity during motion from $A$ to $B$ are respectively ..........

If the body is moving in a circle of radius $ r$ with a constant speed $v$, its angular velocity is

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

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant.  Which of the following is true?  

A particle is released on a vertical smooth semicircular track from point $X$ so that $OX$ makes angle $\theta $ from the vertical ( see figure). The normal reaction of the track on the particle vanishes at point $Y$ where $OY$ makes angle $\phi $ with the horizontal. Then