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A spring of length 'L' is cut into 5 equal parts if initial spring stiffness was R the final stiffness after
parallel combination of all 5 parts will be
parallel combination of all 5 parts will be
- a)R/5
- b)R
- c)5R
- d)25R
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A spring of length 'L' is cut into 5 equal parts if initial sp...
Explanation:
When a spring is cut into equal parts, each part will have the same length, L/5. However, the cross-sectional area of each part will be smaller, since the total cross-sectional area of the spring is divided among the parts. Let us assume that the cross-sectional area of each part is A. Then, the cross-sectional area of the original spring is 5A.
When the parts are combined in parallel, the total cross-sectional area is the sum of the cross-sectional areas of the parts. Therefore, the total cross-sectional area of the combined spring is 5A+5A+5A+5A+5A=25A.
The stiffness of a spring is proportional to its cross-sectional area. Therefore, the stiffness of each part of the spring is R/A, and the stiffness of the combined spring is:
R_combined = (5R/A)+(5R/A)+(5R/A)+(5R/A)+(5R/A)
= (25R/A)
The cross-sectional area of each part is smaller than the cross-sectional area of the original spring, so A<5a. therefore,="" r_combined="">5R, which means that the final stiffness after parallel combination of all 5 parts is 25R.
Therefore, the correct answer is option D, 25R.
When a spring is cut into equal parts, each part will have the same length, L/5. However, the cross-sectional area of each part will be smaller, since the total cross-sectional area of the spring is divided among the parts. Let us assume that the cross-sectional area of each part is A. Then, the cross-sectional area of the original spring is 5A.
When the parts are combined in parallel, the total cross-sectional area is the sum of the cross-sectional areas of the parts. Therefore, the total cross-sectional area of the combined spring is 5A+5A+5A+5A+5A=25A.
The stiffness of a spring is proportional to its cross-sectional area. Therefore, the stiffness of each part of the spring is R/A, and the stiffness of the combined spring is:
R_combined = (5R/A)+(5R/A)+(5R/A)+(5R/A)+(5R/A)
= (25R/A)
The cross-sectional area of each part is smaller than the cross-sectional area of the original spring, so A<5a. therefore,="" r_combined="">5R, which means that the final stiffness after parallel combination of all 5 parts is 25R.
Therefore, the correct answer is option D, 25R.
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A spring of length 'L' is cut into 5 equal parts if initial sp...
For parallel combination of springs the stiffness is equal fo sum of all the stiffness involved in parallel combination so (5+5+5+5+5)R =25R
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A spring of length 'L' is cut into 5 equal parts if initial spring stiffness was R the final stiffness afterparallel combination of all 5 parts will bea)R/5b)Rc)5Rd)25RCorrect answer is option 'D'. Can you explain this answer?
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