The potential energy of a spring when stretched by `2cm is U` if the spring is stretched by `8cm` the potential energy in it is

Options

A. `U/4`
B. `4U`
C. `8U`
D. `16U`

Answer

`(4)`

Explanation

Potential energy of a spring =` 1/2 xx "force constant" xx ("extension")^(2)`
`therefore "Potential energy" infty (extension)^(2)` or , `U_(1)/U_(2) = (x_(1))/(x_(2))^(2)` or , `(U_(1))/(U_(2)) = (2/8)^(2)` or ` (U_(1))/(U_(2)) = 1/16` or , `U_(2) = 16U_(1) = 16U`. `(because U_(1) = U)`