Two spring of force constants `K_(1) and K_(2) (K_(1)gtK_(2))` are stretched by same force. If `W_(1) and W_(2)` be the work done stretching the spring then……..

Options

A. `W_(1) = W_(2)`
B. `W_(1) lt W_(2)`
C. `W_(1) gtW_(2)`
D. `W_(1) = W_(2) = 0`

Answer

B

Explanation

`W_(1) lt W_(2)`
`F_(1) = K_(1)x_(1)` and `F_(2) = K_(2)x_(2)`
Force is same.
`:. K_(1)x_(1)= K_(2)x_(2)`
`:. x_(1) lt x_(2) ( :' K_(1) gt K_(2))`
Work done, `W_(1) = 1/2K_(1)x_(1)^(2)` and `W_(2) = (1)/(2) K_(2)x_(2)^(2)`
`:. W_(1) gt W_(2) ( :' K_(1) gt K_(2) "and" x_(1) lt x_(2))`