Two spreings A and B`(k_A=2k_B)` ar stretched by applying forces of equa magnitudes at the foru ends. If the energy stored in A is E, that in B is

Options

A. `(U)/(2)`
B. `2U`
C. `U`
D. `(U)/(4)`

Answer

B

Explanation

`k_x=2k_0`,`k_y=k_0`
`F=k_(x)x=k_(y)y`
`x=(F)/(2k_0)`,`y=(F)/(k_0)`
`U=(1)/(2)k_(x)x^2=(1)/(2)xx2k_0((F)/(2k_0))^2=(F^2)/(4k_0)`
`U^(')=(1)/(2)k_(y)y^2=(1)/(2)xxk_0((F)/(k_0))^2=(F^2)/(2k_0)`
`(U^('))/(U)=2impliesU^(')=2U`