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Pendulum Loops Around A Nail

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A pendulum of mass M is attached to a string of length L. The other end of the string is attached to pivot point P. The string and mass are held horizontal and released so that the mass swings down. When the mass is at its lowest point, the string hits a nail a distance h above the mass, so that the mass loops around the nail. What the distance can h be above the mass, so that the string remains taut even when the mass loops to a point right above the nail? (NOTE: the string is taut as long as there is tension in the string).

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Solution includes equations, calculations and explanation. 130 words.

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Because, the mass is released from horizontal position, therefore when reaches at the bottom most point, the initial potential energy is converted into K.E.
m*g*L = (1/2)*m*vb^2
=> vb = ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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