Question

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

• A. $\sqrt{2g\left(h+2R\right)}$
• B. $\frac{5}{2}R$
• C. $\sqrt{g\left(5R-2h\right)}$
• D. $\sqrt{2g\left(2R-h\right)}$

Answer 1

Answer: (D)

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