# Report for modulus of rigidity of wire by using solid cylindrical rod

- Report should contain following points
- theory background
- Mathematical formulation
- Apparatus
- Procedure
- Observations
- Calculations
- Error
- Conclusion
over 1 year ago
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## 4 replies

over 1 year ago
Modulus of Rigidity can be measured using a solid cylindrical rod with a wire attached to it. The wire is then pulled with a force and the displacement of the wire can be measured. The Modulus of Rigidity is then calculated using the following formula:
G = (F * L) / (A * δ)
Where:
G = Modulus of Rigidity
F = Applied Force
L = Length of Wire
A = Cross-sectional Area of Wire
δ = Displacement of Wire
The Modulus of Rigidity of the wire can be calculated by measuring the force, length of the wire, cross-sectional area of the wire and displacement of the wire. The wire should be of uniform thickness and length for accurate results. Once these measurements are taken, the Modulus of Rigidity can be calculated.

The following are the details that are needed to calculate the Modulus of Rigidity of a wire using a solid cylindrical rod:
1. Applied Force: The force that is applied to the wire needs to be determined. This can be calculated by measuring the weight of an object suspended from the wire and dividing it by the cross-sectional area of the wire.
2. Length of Wire: The length of the wire should be measured in order to calculate the Modulus of Rigidity. 3. Cross-sectional Area of Wire: The cross-sectional area of the wire should be measured in order to calculate the Modulus of Rigidity.
4. Displacement of Wire: The displacement of the wire should be measured in order to calculate the Modulus of Rigidity. This can be done by measuring the distance between the point where the wire is attached to the solid cylindrical rod and the point where the wire is pulled.
Once all of the measurements are taken, the Modulus of Rigidity of the wire can be calculated using the formula given above.
over 1 year ago
The modulus of rigidity, also known as the shear modulus, is a measure of a material's resistance to deformation under shear stress. It is commonly used to determine the stiffness of a wire. The modulus of rigidity can be determined experimentally using a solid cylindrical rod.
Theory Background: The modulus of rigidity can be determined using the formula, G = (T/J) x L/Δy, where T is the applied torque, J is the polar moment of inertia, L is the length of the rod, and Δy is the shear deformation.
Mathematical Formulation: G = (T/J) x L/Δy
Apparatus:
- Solid cylindrical rod
- Torque wrench
- Dial gauge
- Support stand
- Weight hanger
Procedure:
1. Secure the cylindrical rod in the support stand with the axis of the rod parallel to the ground.
2. Measure the diameter and length of the rod and calculate the polar moment of inertia, J.
3. Attach the weight hanger to the end of the rod and add weights to it until a desired torque is achieved.
4. Measure the shear deformation using the dial gauge.
5. Repeat the procedure for different weight loads to get multiple data points.
Observations:
- Diameter of the rod: d = mm
- Length of the rod: L = mm
- Applied torque: T = Nm
- Shear deformation: Δy = mm
Calculations:
1. Polar moment of inertia, J = π/4 x d^4
2. Modulus of rigidity, G = (T/J) x L/Δy
Error:
- The error in the measurement of the diameter and length of the rod can affect the calculated value of the polar moment of inertia.
- The error in the measurement of the applied torque and shear deformation can also affect the calculated value of the modulus of rigidity.
Conclusion: The modulus of rigidity of the wire can be determined experimentally using a solid cylindrical rod. The procedure involves applying a torque to the rod and measuring the resulting shear deformation. The modulus of rigidity can then be calculated using the formula, G = (T/J) x L/Δy. The accuracy of the results may be affected by errors in the measurement of the diameter, length, torque, and shear deformation