A heavy particle hanging from a string of length $\ell$ is projected horizontally from equilibrium position with speed $\sqrt{\mathrm{g}\ell }$. The speed of the particle at the point where the tension in the string equals weight of the particle is :-

A particle of mass $m$ is attached at the end $\mathrm{B}$ of uniform rod of same mass $m$ and length $l$. If the rod is whirled in vertical circle about end $\mathrm{A}$. What is minimum speed of particle at end $\mathrm{B}$, required to move it in vertical circle ?