A spring of force constant k is cut into lengths of ratio 1: 2: 3 . They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k". Then k' : k" is

Let us assume, the length of spring be l. When we cut the spring into ratio of length 1: 2: 3, we get three springs of lengths l6,2l6 and 3l6 with force constant,∴  k1=kll1=kll/6=6kk2=kll2=kl2l/6=3kk3=kll3=kl3l/6=2kWhen connected in series, 1k'=16k+13k+12k=1+2+36k=1k∴k'=k When connected in parallel, k''=6k+3k+2k=11k k'k''=k11k=111