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'. If they are connected in parallel and force constant is k'', then k' : k'' is   [NEET 2017]

When the spring is cut into pieces, they will have the new force constant. The spring is divided into 1 : 2 : :3 ratio. When the pieces are connected in series, the resultant force constant will be given by1k'=1k1+1k2+1k31k'=1x+12x+13x⇒k'=6x11In parallel, the net force constant,k''=x+2x+3x=6xThe required ratio  k'k''=6x/116x=1:11