when a loads of 10 kg is hang from one end of a wire of length 5m. the wire elongated by 5mm.if the Young's modulus for the material of the wire is 9.8*10^10 . the find the area of the cross section of the wire
Hello aspirant,
To find the area of the cross-section of the wire, we can use the formula for Young's modulus:
Y = (F * L) / (A * ΔL)
where:
- Y is Young's modulus
- F is the force applied (weight of the load)
- L is the original length of the wire
- A is the cross-sectional area of the wire
-
ΔL is the change in length of the wire
We can rearrange the formula to solve for A:
A = (F * L) / (Y * ΔL)
Given:
- F = 10 kg * 9.81 m/s² = 98.1 N
- L = 5 m
- Y = 9.8 * 10^10 N/m²
-
ΔL = 5 mm = 0.005 m
-
Substituting the values into the formula:
A = (98.1 N * 5 m) / (9.8 * 10^10 N/m² * 0.005 m)
Calculating:
A ≈ 1.00 * 10^-6 m²
Therefore, the area of the cross-section of the wire is approximately 1.00 * 10^- 6 square meters . (https://unacademy.com/content/cbse-class-11/study-material/physics/youngs
I hope this helps you.
Calculating the Area of Cross-Section of the Wire
Understanding the Problem:
We have a wire with a known length, load, elongation, and Young's modulus. Our goal is to find the wire's cross-sectional area.
Relevant Formula:
The formula for Young's modulus (Y) is:
Y = (F * L) / (A * ΔL)
Where:
- Y = Young's modulus
- F = Force applied (weight of the load)
- L = Original length of the wire
- A = Cross-sectional area of the wire
- ΔL = Change in length of the wire
Given Values:
- F = 10 kg * 9.8 m/s² = 98 N (converting mass to weight)
- L = 5 m
- ΔL = 5 mm = 0.005 m
- Y = 9.8 * 10^10 N/m²
Rearranging the Formula to Solve for A:
A = (F * L) / (Y * ΔL)
Substituting the Given Values:
A = (98 N * 5 m) / (9.8 * 10^10 N/m² * 0.005 m)
Calculating the Area:
A = 10^-6 m²
Therefore, the cross-sectional area of the wire is 10^-6 square meters.
hope this helps you!!
