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A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal to
- a)strain in the wire
- b)stress in the wire
- c)volume of the wire
- d)Young's modulus of the wire
Correct answer is option 'C'. Can you explain this answer?
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A metallic wire is suspended by attaching some weight to it. If α is t...
Explanation:
When a weight is attached to a metallic wire, it undergoes a longitudinal strain, which is given by:
α = (change in length/original length)
The elastic potential energy stored in the wire is given by:
U = 1/2 * Y * A * α^2
where Y is Young's modulus of the wire, A is the cross-sectional area of the wire, and α is the longitudinal strain.
The energy density of the wire is given by:
ρ = U/V
where V is the volume of the wire.
Therefore, the ratio of elastic potential energy to energy density is given by:
U/ρ = (1/2 * Y * A * α^2)/V
= (1/2 * Y * α^2) * (A/V)
But A/V is the cross-sectional area of the wire, which is constant for a given wire.
Therefore, U/ρ is proportional to α^2.
Thus, the correct option is (C) volume of the wire.
When a weight is attached to a metallic wire, it undergoes a longitudinal strain, which is given by:
α = (change in length/original length)
The elastic potential energy stored in the wire is given by:
U = 1/2 * Y * A * α^2
where Y is Young's modulus of the wire, A is the cross-sectional area of the wire, and α is the longitudinal strain.
The energy density of the wire is given by:
ρ = U/V
where V is the volume of the wire.
Therefore, the ratio of elastic potential energy to energy density is given by:
U/ρ = (1/2 * Y * A * α^2)/V
= (1/2 * Y * α^2) * (A/V)
But A/V is the cross-sectional area of the wire, which is constant for a given wire.
Therefore, U/ρ is proportional to α^2.
Thus, the correct option is (C) volume of the wire.
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A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. Can you explain this answer?
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A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. 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 A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. Can you explain this answer?.
A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. 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 A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metallic wire is suspended by attaching some weight to it. If α is the longitudinal strain and Y is Young's modulus, then the ratio between elastic potential energy and the energy density is equal toa)strain in the wireb)stress in the wirec)volume of the wired)Young's modulus of the wireCorrect answer is option 'C'. Can you explain this answer?.
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