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Two springs with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.
- a)1 : 4
- b)1 : 2
- c)2 : 1
- d)4 : 1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two springs with spring constant K1 and K2 are stretched by the same f...
We know,
Potential energy stored in the spring,
Therefore,
This is the required solution.
Potential energy stored in the spring,
Therefore,
This is the required solution.
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Two springs with spring constant K1 and K2 are stretched by the same f...
Given:
- Two springs with spring constants K1 and K2 are stretched by the same force.
- The potential energy stored in the two springs respectively is U1 and U2.
- The ratio U1: U2 is given to be 1 : 2.
To find:
The ratio of the spring constants K1 : K2.
Explanation:
The potential energy stored in a spring is given by the formula:
U = (1/2) * K * x^2
Where U is the potential energy, K is the spring constant, and x is the displacement from the equilibrium position.
Let's assume that the displacement of both springs is the same, denoted by x.
For the first spring, we have U1 = (1/2) * K1 * x^2
For the second spring, we have U2 = (1/2) * K2 * x^2
Given that U1: U2 = 1 : 2, we can write:
U1/U2 = (1/2) * K1 * x^2 / (1/2) * K2 * x^2
Cancelling out the common terms, we get:
U1/U2 = K1/K2
Since U1: U2 = 1 : 2, we have:
1/2 = K1/K2
Cross-multiplying, we get:
2K1 = K2
Therefore, the ratio of the spring constants K1 : K2 is 2 : 1.
Answer:
The ratio of the spring constants K1 : K2 is 2 : 1. (Option C)
- Two springs with spring constants K1 and K2 are stretched by the same force.
- The potential energy stored in the two springs respectively is U1 and U2.
- The ratio U1: U2 is given to be 1 : 2.
To find:
The ratio of the spring constants K1 : K2.
Explanation:
The potential energy stored in a spring is given by the formula:
U = (1/2) * K * x^2
Where U is the potential energy, K is the spring constant, and x is the displacement from the equilibrium position.
Let's assume that the displacement of both springs is the same, denoted by x.
For the first spring, we have U1 = (1/2) * K1 * x^2
For the second spring, we have U2 = (1/2) * K2 * x^2
Given that U1: U2 = 1 : 2, we can write:
U1/U2 = (1/2) * K1 * x^2 / (1/2) * K2 * x^2
Cancelling out the common terms, we get:
U1/U2 = K1/K2
Since U1: U2 = 1 : 2, we have:
1/2 = K1/K2
Cross-multiplying, we get:
2K1 = K2
Therefore, the ratio of the spring constants K1 : K2 is 2 : 1.
Answer:
The ratio of the spring constants K1 : K2 is 2 : 1. (Option C)
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Two springs with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. 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 with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. 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 with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. Can you explain this answer?.
Two springs with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. 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 with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. 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 with spring constant K1 and K2 are stretched by the same force. If the potential energy stored in the two springs respectively is U1 and U2 and the ratio U1: U2 is given to be 1 : 2, find the ratio of the spring constants K1 : K2.a)1 : 4b)1 : 2c)2 : 1d)4 : 1Correct answer is option 'C'. Can you explain this answer?.
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