KE

ke of the system is NOT the ke of com ..
rather ...it is the sum of ke of all individual particles.

an objective approach :
consider a system : 2 particles each of mass m, one at rest and other with vel v.( same dxn)
ke of the system = 1/2 mv^2
ke of com = 1/2(2m) (v/2)^2 = 1/4 mv^2
this implies ---> ke of system is greater than ke of com ..

consider the same system : but now they both move with vel v ( same dxn)
this time ..u will find that ke of com = ke of system.

hence : ke of system is greater than or equal to ke of com (learn it)
option (c)

guess ..it wasnt that objective.
@dimensions ..yeah!!

just to add to that, when μ=0 , the compression in the spring is maximum when the kinetic energy of the system is minimum.
i.e velocity of each particle is equal to that of V_cm