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Question: With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a he...

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

2g(h+2R)\sqrt{2g(h + 2R)}

B

52\frac{5}{2} R

C

g(5R–2h)\sqrt{g(5R–2h)}

D

2g(2R–h)\sqrt{2g(2R–h)}

Answer

2g(2R–h)\sqrt{2g(2R–h)}

Explanation

Solution

To reach at highest point of tube.

Final velocity , v = 0

\ 12\frac{1}{2} mv2 + mgh = mg (2R)

̃ v = 2g(2R–h)\sqrt{2g(2R–h)}