A bucket is whirled in a vertical circle with a string attached to it. The water in a bucket does not fall down even when the bucket is inverted at the top of its path. In this position choose most appropriate option if $v$ is the speed at the top.

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

A spot light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 \mathrm{rad} {\mathrm{s}}^{-1}$. The spot of light $P$ moves along the wall at a distance $3 \mathrm{m}$. What is the velocity of the spot $P$ when $\mathrm{\theta } = 45°$?