The length of a spring is l and its force constant is k . When a weight W is suspended from it, its length increases by x . If the spring is cut into two equal parts and put in parallel and the same weight W is suspended from them, then the extension will be

Options

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

Answer

A

Explanation

For the spring of length `l, F= Kx therefore x=(F)/(K)`
When the spring is cut into two equal parts, the spring constant of each part =2k and "sin"ce they are joined in parallel, the equivalent spring constant is 2K+2K=4K and "sin"ce the same force (weight) is applied for stretchig,
`x'=(F)/(4K)`
`therefore (x')/(x)=(F)/(4K)xx(K)/(F)=(1)/(4) therefore x'=(x)/(4)`