Two springs of force constants `K_(1)=K_(2)` are stretched by the same force. It `W_(1) " and " W_(2)` are the energies stored its them respectively, then

Options

A. `W_(1) lt W_(2)`
B. `W_(1) gt W_(2)`
C. `W_(1) = W_(2)//2`
D. `W_(1)=W_(2)`

Answer

A

Explanation

The P.E. stored in a spring is given by
`U=(1)/(2)K[(F^(2))/(K^(2))]=(1)/(2)(F^(2))/(K)`
`therefore (U_(1))/(U_(2)) or (W_(1))/(W_(2))=(K_(2))/(K_(1)) (because` F is the same for both)
`because K_(2) lt K_(1) therefore W_(1) lt W_(2)`