The Question is from neet-physics properties-solids-liquids , and it was created by the author VENKATESWARARAO

Question

Two wires of the same material and length but different cross-sectional areas A1 and A2 (A1 > A2) are subjected to the same tensile force. Which wire will experience a greater elongation?

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option B]
## CONCEPT FRAMEWORK
	**Primary Concept**: Elasticity and Hooke's Law
	**Related Topics**: Tensile stress, tensile strain, Young's modulus
	**Prerequisites**: Understanding of stress, strain, and material properties
## SOLUTION PATHWAY
**Given Information**:
		- Wires are of the same material and length
		- Cross-sectional areas: A1 and A2 where A1 > A2
		- Both wires subjected to the same tensile force (F)
**Method & Steps**:
	1. Identify the relevant formulas for elongation.
		Reasoning: The elongation (ΔL) of a wire under tensile stress can be described by the formula:
		$$ \Delta L = \frac{F L}{A Y} $$
		where F is the force, L is the original length, A is the cross-sectional area, and Y is Young's modulus.
	2. Compare the elongation of both wires.
		Working: For wire 1 (A1) and wire 2 (A2):
		$$ \Delta L_1 = \frac{F L}{A_1 Y} $$
		$$ \Delta L_2 = \frac{F L}{A_2 Y} $$
		Since A1 > A2, it follows that $ \Delta L_1 < \Delta L_2 $.
		Key Point: The wire with the smaller cross-sectional area (A2) will elongate more, as the same force results in a greater strain.
	3. Conclude with the comparison of elongations.
		Result: The wire with cross-sectional area A2 experiences a greater elongation than the wire with area A1.
		Verification: This conclusion aligns with the relationship between stress and strain: lower area results in higher stress, leading to more elongation under the same force.
## OPTION ANALYSIS
[A] :x: The wire with cross-sectional area A1 will experience less elongation due to its larger cross-section.
[B] ✓: The wire with cross-sectional area A2 will experience greater elongation due to its smaller cross-section, resulting in higher stress and strain.
[C] :x: Both wires will not experience the same elongation as their cross-sectional areas differ.
[D] :x: The elongation does not depend on the density of the material; it is determined by the material's Young's modulus and the cross-sectional area among other factors.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing stress and strain: Remember that stress is force per unit area, while strain is the change in length per original length.
		2. Overlooking the effects of cross-sectional area: Always consider how area impacts stress and elongation under the same force.
	**Quick Tips**:
		1. When comparing materials or shapes, remember that less area under the same load leads to greater elongation.
		2. Use the relationship between stress and strain to derive conclusions about material behavior under load.

VENKATESWARARAO · Answer

The wire with cross-sectional area A1

VENKATESWARARAO · Answer

The correct Option is "The wire with cross-sectional area A2"

VENKATESWARARAO · Answer

Both wires will experience the same elongation

VENKATESWARARAO · Answer

The elongation depends on the density of the material

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