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 )