The bob of a pendulum of mass m and length L is displaced, 90^∘ from the vertical and gently rel

step 1 This problem covers the concept of conservation of energy and circular motion. Now from the cons

The bob of a pendulum of mass m and length L is displaced,...

The bob of a pendulum of mass $m$ and length $L$ is displaced, $90^{\circ}$ from the vertical and gently released. In order that the string may not break upon passing through the lowest point, its minimum strength must be (a) $m g$ (b) $2 \mathrm{mg}_{\mathrm{J}}$ (c) $3 \mathrm{mg}$ (d) $4 \mathrm{mg}$

The bob of a pendulum of mass $m$ and length $L$ is displaced, $90^{\circ}$ from the vertical and gently released. In order that the string may not break upon passing through the lowest point, its minimum strength must be
(a) $m g$
(b) $2 \mathrm{mg}_{\mathrm{J}}$
(c) $3 \mathrm{mg}$
(d) $4 \mathrm{mg}$

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Key Concepts

Conservation of Energy

This concept involves the conversion of gravitational potential energy to kinetic energy during the motion of the pendulum. As the bob is released from a height, its initial potential energy transforms into kinetic energy as it swings downward, which allows us to calculate its velocity at different positions along its path.

Centripetal Force

In circular motion, an object requires a centripetal force to maintain its curved trajectory. At the lowest point of the pendulum's swing, the tension in the string not only supports the weight of the bob but also provides the necessary centripetal force to keep the bob moving in a circular path.

Tension Analysis in a Pendulum

Analyzing the forces in a pendulum involves determining that the tension at the bottom of the swing is the sum of the gravitational force and the centripetal force. This combined force calculation is essential in determining the minimum strength required for the string to withstand the dynamic forces involved.

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