1.

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

Answer» Correct Answer - D
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)`


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