Work Energy Power

A particle of mass $m$ is attached to a fixed point $A$ by a light, inelastic string of length $R.$ Initially, the particle is projected horizontally with speed just small enough to ensure that the string does not break when it is projected. On becoming horizontal, the string comes in contact with a fixed horizontal peg $B$ at a distance of $R-r$ from $A,$ and the particle begins to rotate about $B.$

Find the minimum horizontal speed of $m$ for which the string breaks after contact with the peg.