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  4. A peg is placed directly below the pendulum’s point of support at a distance l = 0.5 m from the lowest point of the pendulum swing as shown in the fig. The minimum height h from which the pendulum can be released such that the string remains taut for at least one full revolution around the peg is <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9052029efb554ba7e5e5fdb541ac2c51-.png />

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Q. A peg is placed directly below the pendulum’s point of support at a distance $l = 0.5\, m$ from the lowest point of the pendulum swing as shown in the fig. The minimum height h from which the pendulum can be released such that the string remains taut for at least one full revolution around the peg is
image

Work, Energy and Power

Solution:

Critical velocity at highest point $=\sqrt{lg}$ conservation of energy at the starting point and at the highest point implies
$\therefore m g h =m g 2 l+\frac{1}{2} m v^{2}$
$=m g 2 l+\frac{1}{2} m l g=m g l$
$h =\frac{5}{2} l=1.25\, m$