A spring is of spring constant `k=15 N//cm`. It is cut into 3 equal parts, which are joined in parallel. What is the spring constant of the combination ?

Explanation

Let k be the spring constant each of the three parts into which the spring is cut. As initially these three parts of spring are connected in series, so
`(1)/(K)=(1)/(k)+(1)/(k)+(1)/(k)=(3)/(k) or k=3K`
When these three parts of a spring are connected in parallel, the effective spring constant `K^(')` is the given by
`K^(')=k+k+k=3k=3xx3K=9K`
`=9xx15=135N//cm. `