A block of mass m moving with a velocity v0 collides with a stationary block of mass M at the back of which a spring of spring constant k is attached, as shown in the figure. Select the correct alternative(s)

Since, vcm=mvo+M(0)m+M=mvom+MSo, OPTION (A) is correct.At the time of maximum compression both the blocks will be moving with same common velocity. Applying Law of Conservation of Linear Momentum and Conservation of Mechanical Energy, we getmvo=(M+m)v    .......(1)12mvo2=12(M+m)v2+12kxmax2   ......(2) Solving (1) and (2), we getxmax=vomM(m+M)1kSo, OPTION (C) is also correct.In the state of maximum compression, both the blocks are moving with the same velocity. Therefore, velocity of centre of mass in the CM frame is zero.Hence OPTION (D) is also correct.