A system consisting of two blocks of masses m1  and  m2 connected by a spring of spring constant K. A force  F is applied on  m1 along its weight and removed such that  m2 is just lifted. Then F is

For m1  :  F+m1g=kx0                F+m1gk=x0    →1       For  m1 :  m2 to lift                  kx=m2g→2                          Loss of potential energy  of spring= gain of potential energy of blocks12kx20−x2=m1gx0+x12kx0−x=m1gkx0−kx=2m1gF+m1g−m2g=2m1gF=m1+m2gF=m1+m2g