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A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?
  • a)
    1.4 mm
  • b)
    10 mm
  • c)
    1.5 mm
  • d)
    12.4 mm
Correct answer is option 'A'. Can you explain this answer?
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A circular steel wire 2.00 m long must stretch no more than 0.25 cm wh...
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A circular steel wire 2.00 m long must stretch no more than 0.25 cm wh...
Given:

- Length of circular steel wire, l = 2.00 m
- Maximum stretch allowed, Δl = 0.25 cm = 0.0025 m
- Tensile force applied, F = 400 N

To find: Minimum diameter required for the wire

Formula used:

- Young's modulus of elasticity, Y = (F/A) / (Δl/l)
- Cross-sectional area of wire, A = πd²/4

Calculation:

- Substitute the given values in the formula for Young's modulus:

Y = (400/A) / (0.0025/2.00)

- Substitute the formula for cross-sectional area in the above equation:

Y = (400/πd²/4) / (0.0025/2.00)

- Simplify the above equation:

Y = 32,000,000/d²

- Solve for diameter, d:

d² = 32,000,000/Y

d = √(32,000,000/Y)

- Substitute the value of Young's modulus for steel, Y = 2.0 x 10¹¹ N/m²:

d = √(32,000,000/2.0 x 10¹¹)

d = 0.0014 m = 1.4 mm

Therefore, the minimum diameter required for the wire is 1.4 mm.

Answer: (a) 1.4 mm
Community Answer
A circular steel wire 2.00 m long must stretch no more than 0.25 cm wh...
First we should know Young's Modulus of steel then apply its formula
change in length is 0.25cm
l=2m. T=400 A=πr2. then diameter
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Attempt All Questions sub parts from each question.Elasticity vs. plasticity: Objects get deformed when pushed, pulled, and twisted. Elasticity is the measure of the amount that the object can return to its original shape after these external forces and pressure are removed. The opposite of elasticity is plasticity. When something is stretched, and it stays stretched, the material is said to be plastic. Such deformation is said to be plastic deformation. In elastic deformation, atoms of the material are displaced temporarily from their original lattice site. They return back to their original position after the removal of external force. In plastic deformation, atoms of the solid are displaced permanently from their original lattice site. They don’t return back to the original position even after the removal of external load. So, elastic deformation is temporary, whereas plastic deformation is permanent. Amount of elastic deformation is very small. But the amount of plastic deformation is quite large. External force required for elastic deformation of solid is quite small. Force required for plastic deformation is much higher. Total energy absorbed by the material during elastic and plastic deformation region is called modulus of toughness. Energy absorbed by the material during elastic deformation is called module of resilience. Most materials have an amount of force or pressure for which they deform elastically. If more force or pressure is applied, then they undergo plastic deformation. Materials those have a fair amount of plastic deformation before breaking are said to be ductile. Materials those can't stretch or bend much without breaking are said to be brittle. Copper, aluminium etc. are ductile materials. For this reason those are used for making wires. Glass and ceramics are often brittle; they will not bend; they will break.Q. Which of the following statement is false?

Attempt All Questions sub parts from each question.Elasticity vs. plasticity: Objects get deformed when pushed, pulled, and twisted. Elasticity is the measure of the amount that the object can return to its original shape after these external forces and pressure are removed. The opposite of elasticity is plasticity. When something is stretched, and it stays stretched, the material is said to be plastic. Such deformation is said to be plastic deformation. In elastic deformation, atoms of the material are displaced temporarily from their original lattice site. They return back to their original position after the removal of external force. In plastic deformation, atoms of the solid are displaced permanently from their original lattice site. They don’t return back to the original position even after the removal of external load. So, elastic deformation is temporary, whereas plastic deformation is permanent. Amount of elastic deformation is very small. But the amount of plastic deformation is quite large. External force required for elastic deformation of solid is quite small. Force required for plastic deformation is much higher. Total energy absorbed by the material during elastic and plastic deformation region is called modulus of toughness. Energy absorbed by the material during elastic deformation is called module of resilience. Most materials have an amount of force or pressure for which they deform elastically. If more force or pressure is applied, then they undergo plastic deformation. Materials those have a fair amount of plastic deformation before breaking are said to be ductile. Materials those can't stretch or bend much without breaking are said to be brittle. Copper, aluminium etc. are ductile materials. For this reason those are used for making wires. Glass and ceramics are often brittle; they will not bend; they will break.Q. Aluminium is a ............... materials.

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A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?a)1.4 mmb)10 mmc)1.5 mmd)12.4 mmCorrect answer is option 'A'. Can you explain this answer?
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