Two blocks of masses m and $$2m$$ are connected by an ideal spring. The system is placed on smooth horizontal surface. The blocks are given impulse so that the blocks start moving as shown in the figure. In this $$spring-blocks$$ system, find the ratio of the initial kinetic energy of centre of mass to the initial kinetic energy of system w.r.t. centre of mass .

Question

Two blocks of masses m and $$2m$$ are connected by an ideal spring. The system is placed on smooth horizontal surface. The blocks are given impulse so that the blocks start moving as shown in the figure. In this $$spring-blocks$$ system, find the ratio of the initial kinetic energy of centre of mass to the initial  kinetic energy of system w.r.t. centre of mass .

Infinity Learn · Accepted Answer

Velocity of centre of massv→$$cm=(2m)(vi^)+m($$−$$vj^)2m+m$$⇒v→$$cm=v3(2i^$$−$$j^)v$$→$$cm=v34+1=53vKcm=12(m+2m)v$$→$$cm2=123m5v29=56mv2Kinetic$$ energy w.r.t. centre of mass Kint $$=1m1m22m1+m2v$$→$$1$$−v→$$22=12m$$×$$2mm+2m$$|$$vi^$$−$$($$−$$vj^)$$|$$2=23mv2KcmKinternal$$ $$=56mv223mv2=56$$×$$32=1.25$$

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