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A simple pendulum is suspended by a uniform wire of cross-sectional area A and has time period T. If an extra mass M is attached to its bob, the new time period becomes TM. For the wire material with Young’s modulus Y, the value of 1/Y is:

1. [(TM/T)² - 1] A / Mg
2. [1 - (T/TM)²] A / Mg
3. [(T/TM)² - 1] A / Mg
4. [(TM/T)² - 1] Mg / A

Correct answer: [(TM/T)² - 1] A / Mg

Solution

The correct option relates the change in time period due to the added mass to the material properties of the wire, specifically Young's modulus. The formula shows how the increase in time period affects the elongation of the wire, which is directly linked to its Young's modulus, thus providing a relationship between the mechanical properties and the pendulum's behavior.

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