With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a height & so that it may reach the top of the tube? Radius of the tube is R.
 

Velocity of ball to just reach the top of the tube should be given by;
$0 = {\mathrm{v}}^2-2{\mathrm{gh}}_0$
Here ${\mathrm{h}}_0$ = (2R- h)
and in critical case velocity will be zero at top most point.
Thus $\mathrm{v} = \sqrt{2\mathrm{g}(2\mathrm{R}-\mathrm{h})}$