A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and angular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ is $.................$.

A particle is moving in a circle of radius $r$ having centre at $O$, with a constant speed $v$. The magnitude of change in velocity in moving from $A$ to $B$ is

The radius of circle the period of revolution initial position and sense of revolution are indicated in the figure.

$y-$projection of the radius vector of rotating particle $\mathrm{P}$ is

A car goes around uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2 R$ and experiences a centripetal acceleration of magnitude $8 a_c$. Then, its time period is

A particle is moving with a constant speed $v$ in a circle. What is the magnitude of average velocity after half rotation