$[3.](25$ pts $)$ A uniform hollow sphere of mass $M$ and radius $R$ is sliding without rolling on a frictionless table as shown in the figure below.

There is a small lip of height $h$ at the edge of the table.

Find the minimum speed $v($in terms of $R,h,$ and $g)$ such that the sphere tips over and falls off the table.

HINTS:

Use the Parallel$-$Axis Theorem to get the moment of inertia of a uniform hollow sphere about an axis tangent to the sphere.

The sphere undergoes an inelastic collision at the lip.

$($i$)$ Apply Conservation of Angular Momentum immediately before and immediately after the collision.

$($ii$)$ Apply Conservation of Energy after the collision.