Question

With what minimum speed $v$ must a small ball 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 $R$. (Assume radius of the ball is very small).

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

Answer 1

The correct option is D $\sqrt{2g(2R-h)}$

applying the conversation of energy

$mgh+\frac{1}{2}{mv}^2=mg\left(2R\right)$

$V^2=2g(2R-h)$

$V=\sqrt{2g(2R-h)}$