A mass m starting from A reaches B of a frictionless track. On reaching B, it pushes the track with a force equal to x times its weight, then the applicable relation is

KE of blocks at B = PE at A - PE at B 12mv2=mgh−mg2r=mg(h−2r)v2=2g(h−2r)   ...............(i) Also, mv2r=xmg+mg or  v2=(x+1)rg  ............(ii)Equating Eqs. (i) and (ii), we get 2g(h−2r)=(x+1)gr or  2gh=(x+1)gr+4gr=(x+5)grh=x+52r