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  4. A body is suspended from a smooth horizontal nail by a string of length 0.25 metre. What minimum horizontal velocity should be given to it in the lowest position so that it may move in a complete vertical circle with the nail at the centre?

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Q. A body is suspended from a smooth horizontal nail by a string of length $0.25$ metre. What minimum horizontal velocity should be given to it in the lowest position so that it may move in a complete vertical circle with the nail at the centre?

ManipalManipal 2003Work, Energy and Power

Solution:

When a string fixed with a nail, moves along a vertical circle, then the minimum horizontal velocity at the lowest point of circle is given by
$v =\sqrt{5 rg }=\sqrt{5 \times 0.25 \times 9.8}$
$=\sqrt{12.25} m / s$