Final answer:
The tension in the wire equals the weight of the hanging mass when they apply equal torques. At the 5th notch 5 cm away, the tension is one-fifth of the original if the mass stays the same. This is based on equilibrium and torque dynamics.
Step-by-step explanation:
When calculating the tension in the wire on a sonometer, we apply torque concepts. Torque (τ) is the product of force (F) and the perpendicular distance (r) from the axis of rotation to the line of action of the force: τ = F * r. For equilibrium, the torque generated by the hanging mass must equal the torque generated by the tension in the wire.
If both the wire and the first notch are 1 cm away from the axis and applying the same torque, the tension in the wire must be equal to the weight hanging from the tensioning lever. When the lever is moved to the 5th notch, 5 cm away, the distance is five times further from the axis, hence, for equilibrium, the tension in the wire must now be one-fifth of the original tension (assuming the mass on the lever remains unchanged).
This understanding of sonometer, lever, and torque dynamics provides the basis for these calculations and is essential for understanding the physics phenomena involved.