A block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $r$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surface of the block and hemisphere are frictionless.

The height at which the body loses contact with the surface of the sphere 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 ?