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

Answer

C

Explanation

Let extension produced in a spring be is a initial streatched condition spring will have potential energy
`U = (1)/(2) kx^(2)`
Where `k` is spring constant or force constant
`:. (U_(1))/(U_(2)) = (x_(1)^(2))/(x_(2)^(2))`
Given `U_(1) = U, x_(1) = 2 cm, x_(2) = 8 cm`
putting these value in eq (i) we have
`(U)/(U_(1)) = ((2)^(2))/((8)^(2)) = (4)/(64) = (1)/(16)`
`:. U_(1) = 16 U`