JEE Exam > JEE Questions > A wire of length L and cross-section A is mad... Start Learning for Free
A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done is
- a)x Y A/2L
- b)x2YA/L
- c)x2YA/2L
- d)2x2YA/L
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A wire of length L and cross-section A is made of material of Young...
Given, length of wire = L, cross-sectional area = A, Young's modulus = Y, and stretch in the wire = x.
Work done in stretching the wire is given by the formula:
Work done = Force × Distance
When a wire is stretched, a restoring force is created due to the deformation in the wire. This restoring force is proportional to the amount of stretch, and is given by Hooke's law:
F = kx
where F is the restoring force, k is the spring constant (which depends on the material properties of the wire), and x is the amount of stretch.
The work done in stretching the wire can be calculated by integrating the restoring force over the distance stretched:
Work done = ∫ F dx
Substituting F = kx, we get:
Work done = ∫ kx dx
Integrating both sides, we get:
Work done = ½ kx² + C
where C is the constant of integration. We can determine the value of C by setting the initial stretch to zero, i.e., when x = 0, the work done is also zero. This gives:
C = 0
Substituting the value of k from Hooke's law, we get:
Work done = ½ (Y A / L) x²
Simplifying, we get:
Work done = x² YA / 2L
Thus, the correct option is (C).
Work done in stretching the wire is given by the formula:
Work done = Force × Distance
When a wire is stretched, a restoring force is created due to the deformation in the wire. This restoring force is proportional to the amount of stretch, and is given by Hooke's law:
F = kx
where F is the restoring force, k is the spring constant (which depends on the material properties of the wire), and x is the amount of stretch.
The work done in stretching the wire can be calculated by integrating the restoring force over the distance stretched:
Work done = ∫ F dx
Substituting F = kx, we get:
Work done = ∫ kx dx
Integrating both sides, we get:
Work done = ½ kx² + C
where C is the constant of integration. We can determine the value of C by setting the initial stretch to zero, i.e., when x = 0, the work done is also zero. This gives:
C = 0
Substituting the value of k from Hooke's law, we get:
Work done = ½ (Y A / L) x²
Simplifying, we get:
Work done = x² YA / 2L
Thus, the correct option is (C).
Free Test
FREE
| Start Free Test |
Community Answer
A wire of length L and cross-section A is made of material of Young...
Hiii Harshita so In case of rods with given youngs modulus The value of K=YA/2l therefore work done is 1/2kx^2 put value of x which I have given.And here u go with option c Regards
 | Explore Courses for JEE exam |  |
Top Courses for JEEView all
Top Courses for JEE
Question Description
A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer?.
A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A wire of length L and cross-section A is made of material of Young's modulus Y. If it is stretched by an amount x, then work done isa)x Y A/2Lb)x2YA/Lc)x2YA/2Ld)2x2YA/LCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
| Explore Courses for JEE exam | |
Top Courses for JEE
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
