To study the effect of the length of simple pendulum on time and hence find “g” by calculation

 

Abstract

This experiment aims to investigate the relationship between the length of a simple pendulum and the time period of oscillation. By varying the length of the pendulum and measuring the corresponding time periods, the acceleration due to gravity (g) can be calculated.

Introduction

A simple pendulum consists of a mass (bob) suspended from a fixed point (pivot) by a string or rod. The time period of a pendulum's oscillation depends on its length and the acceleration due to gravity (g). This experiment explores this relationship and aims to calculate the value of g.

Procedure

1. Set up a simple pendulum by suspending a bob from a fixed support.
2. Measure the length (\( L \)) of the pendulum from the point of suspension to the center of the bob.
3. Displace the pendulum to a small angle and release it.
4. Measure the time (\( T \)) taken for a certain number of oscillations (\( n \)).
5. Repeat the experiment for different lengths of the pendulum.

Observations and Calculations

Assume the following observations were made during the experiment:

• Length of pendulum (\( L \)): 50 cm
• Time for 10 oscillations (\( T \)): 12.6 seconds
• Number of oscillations (\( n \)): 10

The time period (\( T \)) of one oscillation can be calculated using the formula:

\( T = \frac{{\text{Total time}}}{{\text{Number of oscillations}}} \)

The acceleration due to gravity (\( g \)) can be calculated using the formula:

\( g = \frac{{4\pi^2 \cdot L}}{{T^2}} \)

Conclusion

The experiment demonstrates the inverse relationship between the length of a simple pendulum and its time period of oscillation. By analyzing these relationships, the value of the acceleration due to gravity (g) can be accurately calculated.

Short Questions with Answers

1. What is a simple pendulum?
   Answer: A mass suspended from a fixed point by a string or rod.
2. What factors affect the time period of a pendulum?
   Answer: Length of the pendulum and acceleration due to gravity.
3. What is the formula for calculating the time period of a pendulum?
   Answer: \( T = \frac{{2\pi \cdot \sqrt{L}}}{g} \)
4. What is the relationship between pendulum length and time period?
   Answer: As pendulum length increases, time period increases.
5. How does changing the length of the pendulum affect the value of g?
   Answer: It allows calculation of g using the formula \( g = \frac{{4\pi^2 \cdot L}}{{T^2}} \).
6. What is the SI unit of length?
   Answer: Meter (m).
7. What is the SI unit of time?
   Answer: Second (s).
8. What precautions should be taken during the experiment?
   Answer: Ensure accurate measurements, minimize air resistance, and use a stable support for the pendulum.
9. Why is it important to measure the time for multiple oscillations?
   Answer: To reduce timing errors and obtain a more accurate average time.
10. What is the purpose of displacing the pendulum to a small angle?
    Answer: To ensure simple harmonic motion and accurate results.
11. What is the value of pi (\( \pi \))? Answer: Approximately 3.14159.
12. How does the amplitude of oscillation affect the time period?
    Answer: It does not affect the time period significantly for small angles of oscillation.
13. What is the period of a pendulum?
    Answer: The time taken for one complete oscillation.
14. What is the relationship between the period and frequency of oscillation?
    Answer: They are inversely proportional: \( T = \frac{1}{f} \).
15. Why is it important to repeat the experiment for different lengths of the pendulum?
    Answer: To verify the relationship between pendulum length and time period and to minimize experimental errors.
16. What factors might affect the accuracy of the experiment?
    Answer: Air resistance, friction at the pivot point, and variations in gravitational acceleration at different locations.
17. How can the accuracy of timing measurements be improved?
    Answer: Using a stopwatch with high precision and repeating the timing for multiple oscillations to calculate the average time.
18. What is the significance of using a rigid support for the pendulum?
    Answer: It ensures that the pendulum oscillates along a fixed path without unnecessary movement or wobbling.
19. What is the effect of increasing the length of the pendulum?
    Increasing the length of the pendulum increases the time period of oscillation.
20. How does the value of g vary with location?
    Answer: The value of g varies slightly with location due to differences in gravitational acceleration at different places on Earth.
21. What is the relationship between the period of oscillation and the square root of the length of the pendulum?
    Answer: The period of oscillation is directly proportional to the square root of the length of the pendulum.

MCQs with Answers

1. What is the purpose of varying the length of the pendulum in the experiment?
   1. To test the effect of temperature on pendulum oscillation
   2. To study the effect of length on the time period of the pendulum
   3. To measure the impact of surface friction on pendulum motion
   4. To observe the influence of pendulum material on time period
   Answer: B. To study the effect of length on the time period of the pendulum
2. What happens to the time period of a pendulum if its length is doubled, assuming all other factors remain constant?
   1. It becomes four times larger
   2. It remains the same
   3. It becomes half
   4. It becomes twice as large
   Answer: D. It becomes twice as large
3. How does increasing the length of a pendulum affect its frequency of oscillation?
   1. It decreases the frequency
   2. It increases the frequency
   3. It has no effect on the frequency
   4. It makes the frequency unpredictable
   Answer: A. It decreases the frequency
4. What factor is primarily responsible for the time period of a pendulum?
   1. Mass of the pendulum
   2. Length of the pendulum
   3. Surface area of the pendulum
   4. Material of the pendulum
   Answer: B. Length of the pendulum
5. How does the value of acceleration due to gravity (g) affect the time period of a pendulum?
   1. It has no effect on the time period
   2. It increases the time period
   3. It decreases the time period
   4. It makes the time period unpredictable
   Answer: B. It increases the time period