Question

An inelastic uniform sphere of radius a is sliding without rotation on a smooth horizontal plane when it impinges on a thin horizontal rod at right angles to its direction of motion and at a height b from the plane. Show that it will just roll over the rod if its velocity be 

Answer 1

According to the conservation of energy, the velocity of the sphere must be enough to roll over the rod if the kinetic energy is greater than the potential energy required to lift the sphere up for height b:

$$mv_\text{min}^2/2=mgb,\\ v_\text{min}=\sqrt{2gb}.$$

This is the minimum speed that will let the sphere roll over the rod. Thus, the answer is

$$v\geq\sqrt{2gb}.$$