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Q15OQ

Expert-verifiedFound in: Page 473

Book edition
9th Edition

Author(s)
Raymond A. Serway, John W. Jewett

Pages
1624 pages

ISBN
9781133947271

**A simple pendulum has a period of 2.5 s. (i) what is its period if its length is made four times larger? (a) 1.25 s (b) 1.77 s (c) 2.5 s (d) 3.54 s (e) 5 s (ii) What is its period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger? Choose from the same possibilities.**

(a)The period if its length is made four times larger is${T}_{f}=2{T}_{i}=2\times 2.5s=5s$, Hence option (e) is the correct answer for this question.

(b) The period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger is${T}_{f}={T}_{i}=2.5s$, Hence option (c) is the correct answer for this question.

A simple pendulum of length *L* can be modeled to move in simple harmonic motion for small angular displacements from the vertical. Its period is

$T=2\pi \sqrt{\frac{L}{g}}$

$T=$Period of oscillation

$L=$Length of pendulum

$g=$Gravitational acceleration

From step (1), we have

${T}_{i}=2\pi \sqrt{\frac{{L}_{i}}{g}}$and ${T}_{f}=2\pi \sqrt{\frac{{L}_{f}}{g}}$, where ** i** and

${T}_{f}=2\pi \sqrt{\frac{4{L}_{i}}{g}}\phantom{\rule{0ex}{0ex}}{T}_{f}=2.2\pi \sqrt{\frac{{L}_{i}}{g}}\phantom{\rule{0ex}{0ex}}{T}_{f}=2{T}_{i}\phantom{\rule{0ex}{0ex}}$

The period becomes larger by a factor of 2, to become 5 s.

Hence option (e) is the correct answer for this question.

Changing the mass has no effect on the period of a simple pendulum.

Hence option (c) is the correct answer for this question.

** **

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