A body initially at rest and sliding along a frictionless track from a height $h$ (as shown in the figure) Just completes a vertical circle of diameter $AB=D$. The height $h$ is equal to

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of '$P$' is such that it sweeps out a length $s=t^3+5$, where $s$ is in metres and $t$ is in seconds. The radius of the path is $20 \mathrm{m}$. The acceleration of 'P' when $t=2 \mathrm{s}$ is nearly-

Two particles $A, B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $t=0$, their positions and direction of motion are shown in the figure.

The relative velocity ${\overrightarrow{v}}_A-{\overrightarrow{v}}_B$ at $t=\frac{\pi }{2\mathrm{\omega }}$ is

Three point particles $P$, $Q$ and $R$ move in a circle of the 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 $\mathrm{rad} {\sec }^{-1}$) of $P$, $Q$ and $R$ are $5\mathrm{\pi }$, $2\mathrm{\pi }$ and $3\mathrm{\pi }$, respectively, in the same sense. The time interval after which they all meet is