The reflecting mirror mounted on the moving coil of a vibration galvan...
(a)
Bigger size mirror results in increased inertia constant J.
as J increases both fn & A decrease.
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The reflecting mirror mounted on the moving coil of a vibration galvan...
The Effect of Replacing the Reflecting Mirror on a Vibration Galvanometer
When the reflecting mirror on a moving coil of a vibration galvanometer is replaced by a bigger size mirror, it will result in a lower frequency of resonance and a lower amplitude of vibration. This can be explained by the following factors:
1. Mass of the Mirror:
- When a bigger size mirror is used, it generally has more mass compared to a smaller mirror.
- The mass of the mirror is directly proportional to the inertia of the moving coil system.
- A higher mass will increase the inertia of the system, making it more difficult to set the coil into motion.
- As a result, the natural frequency of resonance of the system decreases.
2. Stiffness of the Spring:
- The vibration galvanometer uses a spring to provide the restoring force for the coil's motion.
- The spring constant represents the stiffness of the spring.
- When a bigger mirror is used, the coil experiences a stronger force due to its increased mass.
- To achieve resonance, the spring needs to provide a force that matches the force exerted by the coil.
- With a bigger mass, the spring has to work harder to provide the required force, resulting in a lower natural frequency of resonance.
3. Damping:
- Damping in a vibration galvanometer is responsible for reducing the amplitude of vibration over time.
- With a bigger mirror, there is a greater air resistance and energy dissipation during each vibration cycle.
- This increased damping effect leads to a decrease in the amplitude of vibration.
Conclusion:
When the reflecting mirror on a moving coil of a vibration galvanometer is replaced by a bigger size mirror, it affects the system's mass, spring stiffness, and damping. The increased mass and corresponding change in spring force result in a lower natural frequency of resonance. Additionally, the increased air resistance and energy dissipation lead to a lower amplitude of vibration. Thus, the correct answer is option 'A': lower frequency of resonance and lower amplitude of vibration.
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