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I'm struggling with a physics question :

What should be the percentage increase in the length of the chord of a pendulum for the period increased by 1%?

The answer is 2%.

I tried with $w = 2 \pi/T = \sqrt{ g/L}$ but no success.

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1 Answer

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What percentage should you increase the area of a square box to increase its side length by 1%?

It's not 1%. Imagine you successfully increase the side length by 1%. Then because area is the square of side length, it increased by a factor $1.01^2 = 1.0201$, or roughly 2%. You must increase the area by 2% to increase the side length by 1%.

Similarly, the length of a pendulum is proportional to the square of its period. (Work this out from the algebra equation you gave.) So length of a pendulum is analogous to area of a box, and period of a pendulum is analogous to side length of a box. Just as with the box, increase one by 2% to increase the other by 1%.

Note that this is an approximation, not an exact result.

This problem is an example of two ideas you should learn well:

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Why do you increase by a factor 1.01^2 and not 1^2? – Justin D. Sep 27 '12 at 1:10
Do you know what percentages are? – Mark Eichenlaub Sep 27 '12 at 1:16
@JustinD., 1% is 0.01. If you increase something by 1%, the new value is 1.01 (101%) times the old value. – Alfred Centauri Sep 27 '12 at 1:16
I feel really stupid :S – Justin D. Sep 27 '12 at 1:25

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