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Question
A small heavy block is attached to the lower end of a light rod of length l which can be rotated about its clamped upper end. What minimum horizontal velocity should the block be given so that it moves in a complete vertical circle?
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Solution
Let the velocity of the body at L is ν.
If the body is moving in a vertical plane then we need to find the minimum horizontal velocity which needs to be given to the body (velocity at L).
Also as point H is the highest point in the vertical plane so horizontal velocity at H will be zero.
\[\frac{1}{2}\text{m} \nu^2 = \text{mgh}\]
\[\frac{1}{2}\text{m} \nu^2 = \text{mg} \left( 2L \right)\]
\[ \Rightarrow \nu = \sqrt{\left( 4 \text{gL} \right)} = 2 \sqrt{\text{gL}}\]
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