InterviewSolution
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InterviewSolution
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Two springs have force constants `K_(1)` and `K_(2)` , where `K_(1)gtK_(2)`. On which spring, more work is downe if (i) they are stretched by the same force? (ii) they are stretched by the same amount? |
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Answer» (i) Under the action of same force F, let the springs be stretched by `x_(1)` and `x_(2)` respectively. `:.F=K_(1)x_(1)=K_(2)x_(2),:. (x_(1))/(x_(2))=(K_(2))/(K_(1))` `(W_(1))/(W_(2))=((1)/(2)K_(1)x_(1)^(2))/((1)/(2)K_(2)x_(2)^(2))=(K_(1))/(K_(2))((x_(1))/(x_(2)))^(2)=(K_(1))/(K_(2))((K_(2))/(K_(1)))^(2)=(K_(2))/(K_(1))` ltBRgt As `K_(1)gtK_(2)` `:. W_(2)gtW_(1)` (ii) When the two springs are stretched by the same distance, say x, then `(W_(1))/(W_(2))=((1)/(2)K_(1)x^(2))/((1)/(2)K_(2)x^(2))=(K_(1))/(K_(2))` As `K_(1)gtK_(2)` therefore `W_(1)gtW_(2)` . |
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