If two springs S, and S, of force constants k, and ky, respectively, are stretched by the same force, it is found that more work is done on spring S, than on spring S.
Statement 1: If stretched by the same amount, work done on S, will be more than that on S.
Statement 2: `k_1` lt`k_2`

Options

A. Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
B. Statement 1 is false, Statement 2 is true.
C. Statement 1 is true, statement 2 is false.
D. Statement 1 is true, statement 2 is true, statement 2 is the correct explanation of statement 1.

Answer

a

Explanation

`k_1x_1=k_2x_2=F`
`w_1=1/2k_1x_1^2=((k_1x_1)^2)/(2k_1)=(F^2)/(2k_1)`
Similarly, `w_2=(F^2)/(2k_2)`
`implies w prop 1/k`
`k_1ltk_2 :. W_1gtw_2`
Statement 2 is true.
Statement `1:w_1=1/2k_1x^2`
`w_2=1/2k_2x^2`
`implies w prop k`
`because k_2gtk_1`
`:. w_2gtw_1`
`:.` Statement 1 is false.