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 $$2017$$]

Question

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 $$2017$$]

Infinity Learn · Accepted Answer

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''$$=6x/116x=1$$:$$11$$

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]

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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]

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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]