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Two wires of same radius and length are subjected to the same load. One wire is of steel and the other is of copper. If Young's modulus of steel is twice that of copper, then ratio of elastic potential energies stored per unit volume in steel wire to that in copper wire is
- a)1 : 2
- b)2 : 1
- c)1 : 4
- d)4 : 1
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
To understand why the answer is option 'A', let's analyze the concept of elastic potential energy stored in a wire.
1. Elastic Potential Energy:
Elastic potential energy is the energy stored in a deformed object when work is done to deform it. In the case of a wire, when it is subjected to a load, it undergoes deformation and stores elastic potential energy.
The elastic potential energy per unit volume (U) in a wire is given by the formula:
U = (1/2) * Y * (strain)^2
where Y is the Young's modulus of the material and strain is the ratio of the change in length to the original length of the wire.
2. Comparison between Steel and Copper Wire:
Let's assume that both the steel and copper wires have the same radius (r) and length (L) and are subjected to the same load.
2.1. Young's Modulus:
Given that the Young's modulus of steel (Y_steel) is twice that of copper (Y_copper), we can write:
Y_steel = 2 * Y_copper
2.2. Strain:
Since both wires are subjected to the same load, the strain in the wires will be the same. Therefore, the strain for both wires can be represented as:
strain_steel = strain_copper = strain (assuming the same load)
2.3. Elastic Potential Energy:
Using the formula for elastic potential energy per unit volume, we can write:
U_steel = (1/2) * Y_steel * (strain_steel)^2
U_copper = (1/2) * Y_copper * (strain_copper)^2
Substituting the values of Y_steel and Y_copper, we get:
U_steel = (1/2) * 2 * Y_copper * (strain)^2
U_copper = (1/2) * Y_copper * (strain)^2
Simplifying the expressions, we find:
U_steel = Y_copper * (strain)^2
U_copper = Y_copper * (strain)^2
3. Ratio of Elastic Potential Energies:
Now, let's calculate the ratio of elastic potential energies stored per unit volume in the steel wire to that in the copper wire:
Ratio = U_steel / U_copper
= (Y_copper * (strain)^2) / (Y_copper * (strain)^2)
= 1
Therefore, the ratio of elastic potential energies stored per unit volume in the steel wire to that in the copper wire is 1:1, which corresponds to option 'A'.
To understand why the answer is option 'A', let's analyze the concept of elastic potential energy stored in a wire.
1. Elastic Potential Energy:
Elastic potential energy is the energy stored in a deformed object when work is done to deform it. In the case of a wire, when it is subjected to a load, it undergoes deformation and stores elastic potential energy.
The elastic potential energy per unit volume (U) in a wire is given by the formula:
U = (1/2) * Y * (strain)^2
where Y is the Young's modulus of the material and strain is the ratio of the change in length to the original length of the wire.
2. Comparison between Steel and Copper Wire:
Let's assume that both the steel and copper wires have the same radius (r) and length (L) and are subjected to the same load.
2.1. Young's Modulus:
Given that the Young's modulus of steel (Y_steel) is twice that of copper (Y_copper), we can write:
Y_steel = 2 * Y_copper
2.2. Strain:
Since both wires are subjected to the same load, the strain in the wires will be the same. Therefore, the strain for both wires can be represented as:
strain_steel = strain_copper = strain (assuming the same load)
2.3. Elastic Potential Energy:
Using the formula for elastic potential energy per unit volume, we can write:
U_steel = (1/2) * Y_steel * (strain_steel)^2
U_copper = (1/2) * Y_copper * (strain_copper)^2
Substituting the values of Y_steel and Y_copper, we get:
U_steel = (1/2) * 2 * Y_copper * (strain)^2
U_copper = (1/2) * Y_copper * (strain)^2
Simplifying the expressions, we find:
U_steel = Y_copper * (strain)^2
U_copper = Y_copper * (strain)^2
3. Ratio of Elastic Potential Energies:
Now, let's calculate the ratio of elastic potential energies stored per unit volume in the steel wire to that in the copper wire:
Ratio = U_steel / U_copper
= (Y_copper * (strain)^2) / (Y_copper * (strain)^2)
= 1
Therefore, the ratio of elastic potential energies stored per unit volume in the steel wire to that in the copper wire is 1:1, which corresponds to option 'A'.
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Two wires of same radius and length are subjected to the same load. One wire is of steel and the other is of copper. If Youngs modulus of steel is twice that of copper, then ratio of elastic potential energies stored per unit volume in steel wire to that in copper wire isa)1 : 2b)2 : 1c)1 : 4d)4 : 1Correct answer is option 'A'. Can you explain this answer?
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Two wires of same radius and length are subjected to the same load. One wire is of steel and the other is of copper. If Youngs modulus of steel is twice that of copper, then ratio of elastic potential energies stored per unit volume in steel wire to that in copper wire isa)1 : 2b)2 : 1c)1 : 4d)4 : 1Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two wires of same radius and length are subjected to the same load. One wire is of steel and the other is of copper. If Youngs modulus of steel is twice that of copper, then ratio of elastic potential energies stored per unit volume in steel wire to that in copper wire isa)1 : 2b)2 : 1c)1 : 4d)4 : 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two wires of same radius and length are subjected to the same load. One wire is of steel and the other is of copper. If Youngs modulus of steel is twice that of copper, then ratio of elastic potential energies stored per unit volume in steel wire to that in copper wire isa)1 : 2b)2 : 1c)1 : 4d)4 : 1Correct answer is option 'A'. Can you explain this answer?.
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