# A small ball starts moving from A over a fixed track as shown in the figure. Surface AB has friction. From A to B the ball rolls without slipping. Surface BC is frictionless. KA, KB and KC are kinetic energies of the ball at A, B and C, respectively. Then[figure]a) hA>hC ; KB> KCb) hA>hC ; KC> KAc) hA = hC ; KB = KCd) hAC ; KB> KC

$\\E_A=mgh_A+K_A \\E_B=K_B \\E_C=mgh_C+K_C \\since the energy is conserved \\E_A=E_C=E_C \\=>K_B>K_A \\=>K_B>K_C \\solving first and last we get \\h_A-h_C=\frac{K_C-K_A}{Mg}$