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Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ is
- a)4/5
- b)5/4
- c)16/25
- d)25/16
Correct answer is option 'B'. Can you explain this answer?
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Two springs, having spring constants of 25 N-m⁻1 and 16 N-m̿...
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Two springs, having spring constants of 25 N-m⁻1 and 16 N-m̿...
Solution:
Given, spring constants of two springs are k1 = 25 N/m and k2 = 16 N/m.
Let F1 and F2 be the forces applied on the springs.
The work done on a spring is given by:
W = (1/2) kx²
where, k is the spring constant and x is the displacement of the spring.
If the work done in stretching the two springs is equal, then we have:
(1/2) k1 x1² = (1/2) k2 x2²
Dividing both sides by x1² and multiplying by x2², we get:
(x2/x1)² = k1/k2
Taking square root on both sides, we get:
x2/x1 = √(k1/k2)
Now, force F is related to displacement x by:
F = kx
Therefore, we have:
F1 = k1 x1 and F2 = k2 x2
Dividing F2 by F1, we get:
F2/F1 = (k2 x2)/(k1 x1)
Substituting x2/x1 by √(k1/k2), we get:
F2/F1 = √(k2/k1)
Substituting the given values of spring constants, we get:
F2/F1 = √(16/25) = 4/5
Therefore, the ratio of the forces F2 and F1 is 5/4.
Hence, option (B) is the correct answer.
Given, spring constants of two springs are k1 = 25 N/m and k2 = 16 N/m.
Let F1 and F2 be the forces applied on the springs.
The work done on a spring is given by:
W = (1/2) kx²
where, k is the spring constant and x is the displacement of the spring.
If the work done in stretching the two springs is equal, then we have:
(1/2) k1 x1² = (1/2) k2 x2²
Dividing both sides by x1² and multiplying by x2², we get:
(x2/x1)² = k1/k2
Taking square root on both sides, we get:
x2/x1 = √(k1/k2)
Now, force F is related to displacement x by:
F = kx
Therefore, we have:
F1 = k1 x1 and F2 = k2 x2
Dividing F2 by F1, we get:
F2/F1 = (k2 x2)/(k1 x1)
Substituting x2/x1 by √(k1/k2), we get:
F2/F1 = √(k2/k1)
Substituting the given values of spring constants, we get:
F2/F1 = √(16/25) = 4/5
Therefore, the ratio of the forces F2 and F1 is 5/4.
Hence, option (B) is the correct answer.
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Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer?.
Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer?.
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Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two springs, having spring constants of 25 N-m⁻1 and 16 N-m⁻1are stretched by forces F₁ and F₂.If work done in stretching the springs is equal, then the ratio of the forces F₁ and F₂ isa)4/5b)5/4c)16/25d)25/16Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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