Let the mass of smaller object be m and mass of larger object be M.
As the kinetic energies are equal,
[tex]\frac{p_m^2}{2m}=\frac{p^2_{_M}}{2M}[/tex]On solving further,
[tex]\frac{p_m}{p_M}=\text{ }\sqrt[]{\frac{m}{M}}[/tex]Hence, option A is correct.