Book edition 9th Edition

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

Pages 1624 pages

ISBN 9781133947271

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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 $T_{f} = 2 T_{i} = 2 \times 2.5 s = 5 s$ , 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 $T_{f} = T_{i} = 2.5 s$ , Hence option (c) is the correct answer for this question.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Relationship between the length and time

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

$T = 2 π \sqrt{\frac{L}{g}}$

$T =$ Period of oscillation

$L =$ Length of pendulum

$g =$ Gravitational acceleration

Step 2(i): Find the period if its length is made four times larger

From step (1), we have

$T_{i} = 2 π \sqrt{\frac{L_{i}}{g}}$ and $T_{f} = 2 π \sqrt{\frac{L_{f}}{g}}$ , where i and f stands for initial and final respectively.

$T_{f} = 2 π \sqrt{\frac{4 L_{i}}{g}} T_{f} = 2.2 π \sqrt{\frac{L_{i}}{g}} T_{f} = 2 T_{i}$

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

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

Step 3(ii): Find the period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger

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

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

Find Study Materials for

Create Study Materials

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Relationship between the length and time

Step 2(i): Find the period if its length is made four times larger

Step 3(ii): Find the period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Physics For Scientists & Engineers

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Relationship between the length and time

Step 2(i): Find the period if its length is made four times larger

Step 3(ii): Find the period if the length is held constant at its initial value and the mass of the suspended bob is made four times larger

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics