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The potential energy of a long spring when stretched by 2 cm is U. If the spring is stretched by 8 cm, potential energy stored in it will be :
- a)4U
- b)8U
- c)16U
- d)2U
Correct answer is option 'C'. Can you explain this answer?
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The potential energy of a long spring when stretched by2cmis U. If the...
Potential Energy of a Stretched Spring
When a spring is stretched or compressed from its equilibrium position, it stores potential energy. The potential energy stored in a spring is given by the equation:
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.
Given Information:
- The potential energy of a long spring when stretched by 2 cm is U.
- The spring is stretched by 8 cm.
Calculating Potential Energy:
Let's calculate the potential energy stored in the spring when it is stretched by 8 cm.
Using the given information, we can write the equation for potential energy as:
U = (1/2) k x^2
Substituting the given values:
U = (1/2) k (8 cm)^2
Simplifying the equation:
U = (1/2) k (64 cm^2)
U = 32 k cm^2
Therefore, the potential energy stored in the spring when stretched by 8 cm is 32 k cm^2.
Comparing Potential Energies:
Now, let's compare the potential energy stored in the spring when it is stretched by 8 cm with the potential energy when it is stretched by 2 cm.
Given: The potential energy of the spring when stretched by 2 cm is U.
Comparing the two potential energies:
32 k cm^2 = 16 times U (since (8 cm)^2 = 64 cm^2 and 64 cm^2 / (2 cm)^2 = 16)
Therefore, the potential energy stored in the spring when stretched by 8 cm is 16 times the potential energy when it is stretched by 2 cm.
Conclusion:
The potential energy stored in the spring when it is stretched by 8 cm is 16U. Therefore, the correct answer is option C.
When a spring is stretched or compressed from its equilibrium position, it stores potential energy. The potential energy stored in a spring is given by the equation:
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.
Given Information:
- The potential energy of a long spring when stretched by 2 cm is U.
- The spring is stretched by 8 cm.
Calculating Potential Energy:
Let's calculate the potential energy stored in the spring when it is stretched by 8 cm.
Using the given information, we can write the equation for potential energy as:
U = (1/2) k x^2
Substituting the given values:
U = (1/2) k (8 cm)^2
Simplifying the equation:
U = (1/2) k (64 cm^2)
U = 32 k cm^2
Therefore, the potential energy stored in the spring when stretched by 8 cm is 32 k cm^2.
Comparing Potential Energies:
Now, let's compare the potential energy stored in the spring when it is stretched by 8 cm with the potential energy when it is stretched by 2 cm.
Given: The potential energy of the spring when stretched by 2 cm is U.
Comparing the two potential energies:
32 k cm^2 = 16 times U (since (8 cm)^2 = 64 cm^2 and 64 cm^2 / (2 cm)^2 = 16)
Therefore, the potential energy stored in the spring when stretched by 8 cm is 16 times the potential energy when it is stretched by 2 cm.
Conclusion:
The potential energy stored in the spring when it is stretched by 8 cm is 16U. Therefore, the correct answer is option C.
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The potential energy of a long spring when stretched by2cmis U. If the...
Fo x = 2
Eq. (2)/eq. (1)
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The potential energy of a long spring when stretched by2cmis U. If the spring is stretched by8cm, potential energy stored in it will be :a)4Ub)8Uc)16Ud)2UCorrect answer is option 'C'. Can you explain this answer?
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The potential energy of a long spring when stretched by2cmis U. If the spring is stretched by8cm, potential energy stored in it will be :a)4Ub)8Uc)16Ud)2UCorrect 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 The potential energy of a long spring when stretched by2cmis U. If the spring is stretched by8cm, potential energy stored in it will be :a)4Ub)8Uc)16Ud)2UCorrect 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 The potential energy of a long spring when stretched by2cmis U. If the spring is stretched by8cm, potential energy stored in it will be :a)4Ub)8Uc)16Ud)2UCorrect answer is option 'C'. Can you explain this answer?.
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