A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at  x=x0+A. In both the cases, a particle with mass m(

When block is placed at a position  x0From conservation of momentum, MV=m+MV1⇒V1=MAωm+M=MAm+MKM ⇒A1KM+m=MAm+MKM ⇒A1=AMm+M ⇒A1A=Mm+M When block is placed at extreme position amplitude does not change since at extreme position  M is at rest . So, initial and final momentums are not changedB) Tinitial=2πMK  After block is placed  Tfinal=2πm+MKC) Total energy   E=12mA2w2=12mVmean2Before block is placedAt  x0:E1=12MV2At  x0+A : E2=12MV2=E1energy constantAfter block is placed At  x0:E3=12m+MMVm+M2 =12MV2Mm+MAt x0+A : E4=E3 [energy constant]As   Mm+M<1 so energy decreasesD) When block is placed at  x0V1=Mm+MV V1