Physics Practical: Effect of Mass on Time Period of a Simple Pendulum

1. Objective

To investigate whether the mass of the pendulum bob affects the time period of oscillation.

2. Apparatus

• Pendulum stand and clamp
• Thread (light and inextensible)
• Metal bobs of different masses (50g, 100g, 200g)
• Stopwatch
• Meter ruler
• Protractor (optional)

3. Theory Background

The time period T of a simple pendulum is given by:

T = 2π√(L/g)

Where:

• T = time period (seconds)
• L = length of the string (meters)
• g = acceleration due to gravity (9.8 m/s²)

This equation shows clearly that T is dependent only on the length L and gravity g. There is no mass variable in the equation, which means mass does not affect the time period of the pendulum. This is what the practical will help to prove.

4. Real Life Application

In real life, pendulums are used in many places. Examples include:

• Clocks: Grandfather clocks use pendulums for time keeping. Changing the bob weight does not affect how the clock keeps time.
• Playground Swings: When children of different weights use swings, the time it takes to swing forward and back is nearly the same if the ropes are the same length.
• Earthquake measuring devices: Use pendulums to sense motion and are calibrated without considering bob mass.

5. Procedure

1. Measure and fix the length of the string to 60 cm.
2. Attach a 50g bob, pull slightly (angle < 15°), release, and time 10 oscillations.
3. Calculate time period T = total time / 10.
4. Repeat for 100g and 200g bobs, keeping length and amplitude constant.
5. Record all readings in a table.

6. Sample Table and Graph

7. Results and Conclusion

• Time period remains nearly constant across all masses.
• Hence, mass does not affect the period of a simple pendulum.
• Time period is only dependent on length and gravity.

8. NECTA Example Questions (Solved)

Example 1 (NECTA 2019 Physics Paper 3)

Question: Using a pendulum of length 60 cm, measure time for 10 oscillations using 3 different bobs: 50g, 100g, 200g. Comment on your results.

Answer:

• 50g: 15.5 sec → T = 1.55 s
• 100g: 15.6 sec → T = 1.56 s
• 200g: 15.4 sec → T = 1.54 s
• Conclusion: Time period remains nearly same → Mass does not affect period.

Example 2 (NECTA 2016 Physics Practical)

Question: What conclusion can be made from an experiment where a pendulum bob of varying mass shows no change in time period?

Answer: The mass of the bob has no effect on the time period. Time period depends only on string length and acceleration due to gravity.

Example 3 (Extra Practice)

Question: A student performed a pendulum experiment with masses 70g, 150g, and 250g. Each trial took approximately 16 seconds for 10 oscillations. What is the period and what conclusion can you draw?

Answer: Time period T = 16 / 10 = 1.6 s. Since all masses gave same time, conclusion: Mass does not affect time period.

9. Summary Notes

• The time period of a pendulum is independent of its mass.
• Only the length of the string and gravity affect the time period.
• Real-life examples like swings and clocks support this theory.
• Graphs plotted with T against mass show a flat line, indicating no relationship.

10. Conclusion for Learners

This experiment teaches an essential concept of oscillation and simple harmonic motion. By practicing it repeatedly and analyzing the graphs, students gain a deeper understanding of real scientific principles. It’s not just about passing NECTA, but truly grasping the way physical systems behave in real life.