Question

Figure shows a smooth track in a vertical plane, consisting of two circular arcs $A B$ and $B C$ of the same radius $R=2\, m$. The common tangent to the arcs, $B D$, is horizontal. A small block placed on the track at a height $h$ above $B D$ leaves the track at exactly the same depth below. Determine $h$ in $cm$.

Answer 1

Condition for leaving contact
$m g\left(\frac{R-h}{R}\right)=\frac{m v^{2}}{R}$ .... (i)
From work energy theorem
$2 m g h=\frac{1}{2} m v^{2}$
$m v^{2}=4 m g h$ .... (ii)
From (i) and (ii), we get
$h=\frac{R}{5}=40 \,cm$