(a) what is the effect on the period of a pendulum if you double its length? (b) what is the effect on the period of a pendulum if you decrease its length by 5.00%?

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09-12-2022
Physics

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(a) what is the effect on the period of a pendulum if you double its length? (b) what is the effect on the period of a pendulum if you decrease its length by 5.00%?

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-16T01:46:09-05:00

The effect on the period of a pendulum if you double its length is the period increases by a factor of √2 and if you decrease its length of a pendulum by 5.00% the period decreases by 2.5%.

A pendulum has an initial period of 2π√L/ g and then it has some new period T2 which is 2π√L2/g

(a) Give that L2 = 2L1

So we'll substitute in 2L1 in place of L2

T2 = 2π√2L1/g = √2T1

So when doubling the length, the period increases by a factor of √2

(b) Given that length of a pendulum decreases by 5.00%

Then length of remaining pendulum = L2 = 95% L1= 0.95L1

T2= 2π√L2/g = 2π√0.95L1/g = √0.95T1 = 0.975T1

Hence it decreases by 2.5%.

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