A smooth track consists of two parts. The left part is straight and is connected to the right circular part at a point at which the tangent of the circle has the same slope as the straight track. The radius of the circular part is R. A point object with mass m is initially at rest on the left straight track at a height of H above ground, as shown in the figure below.

A point target is located at the center of the circular track. The object released at a certain initial height H will hit the target. Find the value of H if R=2m .