Question

Ball $A$ of mass $m$, after sliding from an inclined plane, strikes elastically another ball $B$ of same mass at rest. Find the minimum height $h$ so that ball $B$ just completes the circular motion of the surface at $C$.(All surfaces are smooth.)

• A. $h=\frac{5}{2}R$
• B. $h=2R$
• C. $h=\frac{2}{5}R$
• D. $h=3R$

Answer 1

The correct option is A $h=\frac{5}{2}R$

Using the conservation of energy:

$mgh=\frac{1}{2}m{v}^2+2mgR$

$gh=\frac{v^2}{2}+2gR$

Required velocity at the top $v=\sqrt{gR}$

$gh=\frac{gR}{2}+2gR\Rightarrow h=\frac{5}{2}R$