Two blocks A and B of masses in and 2m, respectively, are connected with the help of a spring having spring constant, k as shown in Fig. Initially, both the blocks arc moving with same velocity v on a smooth horizontal plane with the spring in its natural length. During their course of motion, block B makes an inelastic collision with block C of mass m which is initially at rest. The coefficient of restitution for the collision is 1//2. The maximum compression in the spring is

Two blocks A and B of masses in and 2m, respectively, are connected wi

1.	Two blocks A and B of masses in and 2m, respectively, are connected with the help of a spring having spring constant, k as shown in Fig. Initially, both the blocks arc moving with same velocity v on a smooth horizontal plane with the spring in its natural length. During their course of motion, block B makes an inelastic collision with block C of mass m which is initially at rest. The coefficient of restitution for the collision is 1//2. The maximum compression in the spring is
Answer» `sqrt((2m)/K)` will never be attained `sqrt(m/(12k))v` `sqrt(m/(6k))v` Solution :For collision of `B` and `C` `2mv=2mv_(1)+mv_(2)` `1/2=(v_(2)-v_(1))/vimplies2v_(2)-2v_(1)=v` Solving above equation `v_(1)=v/2` and `v_(2)=v` Now for blocks `A` and `B` plus spring system, using reduced mass concept and applying WORK ENERGY theorem, let maximum compresion in spring be `x_(0)` and that the time of maximum compression relative velocity of blocks be zero. reduced mass is given by `"mu"=(mxx2m)/(3m)=(2m)/3` `0-(muxx(v-v//2)^(2))/2=-(kx_(0)^(2))/2impliesx_(0)=(sqrt(m/(6k)))v`