Concept:The swing duration of an ideal simple pendulum is governed entirely by the length of its string and local gravity, exhibiting a unique property called isochronism.
Formula:$$ T = 2\pi \sqrt{\frac{L}{g}} $$
Solution:- Look closely at the formula for the time period (\( T \)). The variable for mass (\( m \)) does not appear anywhere in the equation.
- Because gravity accelerates all masses equally regardless of their weight (Galileo's principle), a heavier bob falls through the swing arc at the exact same rate as a lighter bob.
- Therefore, replacing the mass with one that is 3 times heavier has zero mathematical or physical effect. The time period remains exactly T.
Why other options are incorrect:Students often confuse pendulum physics with spring-mass systems (where mass
does alter the period). Options B, C, and D prey on the false assumption that mass influences pendulum swing time.
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