JEE Class main Answered

Let k be the spring constant of spring of unstretched length L .

If F is ithe applied force to the spring to extend , then extenstion length x is

  .............................. (1)

Let us consider the full length L of spring consists of two parts so that one part is 4 times of other part .

Hence their individual lengths are (4/5)L and (1/5)L .

Since extension lengths for same applied force is proportional to length , we have

x = (4/5) x + (1/5) x

If extension of longer part is (4/5) x for same applied force  F, then force constant k₁ of this longer part is

if we substitute x from eqn.(1) , then we get from above expression

Hence , from above expression , we get , k₁ = (5/4) k

Hence the longer part of spring has spring constant  (1.25 k )