If a spring of stiffness `'k'` is cut into two parts `'A'` and `'B'` of length `l_(A):l_(B)=2:3`, then the stiffness of spring `'A'` is given by

Options

A. `(5)/(2)k`
B. `(3k)/(5)k`
C. `(2k)/(5)k`
D. `k`

Answer

A

Explanation

If `l` is the total length of spring, then
`l_(A)=(2l)/(5)` and `l_(B)=(3l)/(5)`
If `k_(A), k_(B)` are the stiffness of `A` and `B` , then
or `k_(A)=(kl)/(l_(A))=(kl)/((2l//5))=(5)/(2)k`