Q.

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 .

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answer is 1.25.

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Detailed Solution

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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