1. Aim
To determine the moment of inertia (I) of a given irregular body using a torsion pendulum.
2. Apparatus Used
- Torsion pendulum apparatus
- Irregular body
- Stopwatch
- Vernier caliper / screw gauge
- Meter scale
- Masses and hanger (if applicable)
- Graph paper
3. Diagram
[Insert Diagram Here - Showing torsion wire, platform, and body]
4. Theory
The time period \( T \) of a torsion pendulum is related to the moment of inertia \( I \) and torsional constant \( C \) by:
\[ T = 2\pi \sqrt{\frac{I}{C}} \]
Using time periods with and without body:
\[ I_b = C \left( \frac{T^2 - T_0^2}{4\pi^2} \right) \]
5. Formula
\[ I_b = \frac{C}{4\pi^2}(T^2 - T_0^2) \]
6. Procedure
- Set up the torsion pendulum and balance the platform.
- Measure the time period \( T_0 \) for the platform alone.
- Place the irregular body symmetrically and measure the new time period \( T \).
- Repeat and average readings for accuracy.
- Use known or calculated torsional constant \( C \).
- Calculate the moment of inertia.
7. Observation Table
A. For Platform Alone
| Trial No. | Time for 10 Oscillations (s) | Time Period \( T_0 \) (s) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| Average |
B. For Platform + Body
| Trial No. | Time for 10 Oscillations (s) | Time Period \( T \) (s) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| Average |
8. Calculations
\( T_0 = \ldots \) s, \( T = \ldots \) s, \( C = \ldots \) Nm/rad
\[ I_b = \frac{C}{4\pi^2}(T^2 - T_0^2) \]
9. Result
The moment of inertia of the given body is:
\[ I_b = \boxed{\ldots \ \text{kg} \cdot \text{m}^2} \]
10. Precautions
- Avoid external vibrations.
- Ensure symmetry in body placement.
- Use accurate timing techniques.
- Ensure wire is undamaged.
11. Viva Voce Questions
- Define moment of inertia.
- Explain torsion pendulum operation.
- What is the torsional constant?
- Why is symmetric placement important?