A ball weighing $1 \mathrm{kg}$ is tied to a string of length $l_0=15 \mathrm{cm}$ and the other end of the string is tied to a fixed support. Initially, the ball is held in a position such that the string is horizontal and then it is released. A nail $N$ is situated vertically below the support at a distance $L$. The minimum value of $L$ such that the string will wound round the nail is

A particle of mass $m$ is attached to a light string of length $l$, the other end of which is fixed. Initially, the string is kept horizontal and the particle is given an upward velocity $v$. The particle is just able to complete a vertical circle.

As shown in the figure $BEF$ is a fixed vertical circular tube. A block of mass $m$ starts moving in the tube at the point $B$ with velocity $V$ towards $E$. It is just able to complete the vertical circle, then