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` .

Options

A. `sqrt(2g(h + 2R))`
B. `(5)/(2)R`
C. `sqrt(g(5R - 2h))`
D. `sqrt(2g(2R - h))`

Answer

D

Explanation

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