Two blocks having masses $$8$$ kg and $$16$$ kg are connected to the two ends of a light spring. The system is placed on a smooth horizontal floor. An inextensible string also connects B with ceiling as shown in the figure at the initial moment. Initially the spring has its natural length. A constant horizontal force F is applied to the heavier block as shown. What is the maximum possible value of F (in$$ $$N) so the lighter block does not loose contact with ground.

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Infinity Learn · Accepted Answer

Draw FBD of B to get extension in spring. Instant when block B just looses contact with ground, the net force on it becomes zero. $$kx$$−Tcos⁡θ$$=0$$    ........(i)Tsin$$⁡θ$$+N$$−$$mg=0$$ .......$$(ii)To$$ lift the block B, N $$=$$ $$0$$, from $$(i) and (ii), we get kxcos⁡θ$$sin$$⁡θ$$=mgx=mgktan$$⁡θ$$=80k$$×$$(4/3)=60kIf$$ spring has to just extend till this value at their extension it should be at rest.Now we apply work energy theorem to get $$Fx=12kx2$$⇒$$F=30$$ N

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