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  4. 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.

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Q. 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 $cm$.Physics Question Image

Work, Energy and Power

Solution:

image
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
$h=\frac{R}{5}=40 \,cm$