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A spring of stiffness constant k is cut in two equal parts. The stiffness constant of new spring will be k/2.
- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
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A spring of stiffness constant k is cut in two equal parts. The stiffn...
Explanation: k=Gd⁴/8DᵌN, hence k is inversely proportional to number of coils. Thus result will be 2k.
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A spring of stiffness constant k is cut in two equal parts. The stiffn...
Explanation:
When a spring is cut into two equal parts, each part will have half the number of coils compared to the original spring. This is because the number of coils in a spring is directly proportional to its length.
Stiffness constant (k):
The stiffness constant of a spring is a measure of its ability to resist deformation under an applied force. It is given by the equation k = (Gd^4)/(8ND^3), where G is the modulus of rigidity, d is the wire diameter, N is the number of coils, and D is the mean coil diameter.
Effect of cutting the spring:
When a spring is cut into two equal parts, the number of coils (N) in each part is reduced by half. However, the wire diameter (d) and mean coil diameter (D) remain the same for both parts.
Stiffness constant of the new spring:
Using the equation for the stiffness constant (k), we can see that cutting the spring into two equal parts will not change the stiffness constant.
- The modulus of rigidity (G) is a material property and remains the same for both parts.
- The wire diameter (d) and mean coil diameter (D) are also the same for both parts.
Therefore, the stiffness constant of each part of the spring will remain the same as the original spring, which is k.
Conclusion:
The statement that the stiffness constant of the new spring will be k/2 is false. The stiffness constant of each part of the spring will be equal to the stiffness constant of the original spring, which is k.
When a spring is cut into two equal parts, each part will have half the number of coils compared to the original spring. This is because the number of coils in a spring is directly proportional to its length.
Stiffness constant (k):
The stiffness constant of a spring is a measure of its ability to resist deformation under an applied force. It is given by the equation k = (Gd^4)/(8ND^3), where G is the modulus of rigidity, d is the wire diameter, N is the number of coils, and D is the mean coil diameter.
Effect of cutting the spring:
When a spring is cut into two equal parts, the number of coils (N) in each part is reduced by half. However, the wire diameter (d) and mean coil diameter (D) remain the same for both parts.
Stiffness constant of the new spring:
Using the equation for the stiffness constant (k), we can see that cutting the spring into two equal parts will not change the stiffness constant.
- The modulus of rigidity (G) is a material property and remains the same for both parts.
- The wire diameter (d) and mean coil diameter (D) are also the same for both parts.
Therefore, the stiffness constant of each part of the spring will remain the same as the original spring, which is k.
Conclusion:
The statement that the stiffness constant of the new spring will be k/2 is false. The stiffness constant of each part of the spring will be equal to the stiffness constant of the original spring, which is k.
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A spring of stiffness constant k is cut in two equal parts. The stiffness constant of new spring will be k/2.a)Trueb)FalseCorrect answer is option 'B'. Can you explain this answer?
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