Two springs have their force constants `k_(1)` and `k_(2) (k_(2) gt k_(1)`) . When they are stretched by the same force _____ .

Explanation

Case:I
Suppose, they are stretched by same distance `x_(1)andx_(2)` by the same force F.
Then, `F=k_(1)x_(1)=k_(2)x_(2)`
`(W_(1))/(W_(2))=((1)/(2)k_(1)x_(1)^(2))/((1)/(2)k_(2)x_(2)^(2))=(k_(1).x_(1).x_(1))/(k_(2).x_(2).x_(2))=(F.x_(1))/(F.x_(2))`
`(W_(1))/(W_(2))=(x_(1))/(x_(2))" "...(1)`
Since, `k_(1)x_(1)=k_(2)x_(2)`
`(x_(1))/(x_(2))=(k_(2))/(k_(1))`
Equation (1) becomes,
`(W_(1))/(W_(2))=(k_(2))/(k_(1))`
`W_(1)propk_(1)`
`W_(2)propk_(2)`
Since, `k_(1)gtk_(2)`
`W_(1)gtW_(2)`
Case:II
Suppose strings are stretched by same distance.
`(W_(1))/(W_(2))=((1)/(2)k_(1)x^(2))/((1)/(2)k_(2)x^(2))=(k_(1))/(k_(2))`
since, `k_(1)gtk_(2). W_(1)gtW_(2)`