Physics · Work, Power & Energy

Since K.E is inversely propotional to the mass the ratio of the masses will be inverted and would become 1:4.

This option is incorrect because if the two bodies had their masses in the ratio 1:2 while possessing equal momentum, their kinetic energies would not differ by a factor of four. The relationship between mass and kinetic energy, under constant momentum, is inverse — a smaller change in mass would only cause a smaller change in energy. Hence, a 1:2 mass ratio cannot produce a 4:1 energy ratio.

This option is correct because when two bodies have the same momentum, the one with smaller mass must possess greater kinetic energy. In this case, the body that has four times less mass will have four times greater kinetic energy. The relationship shows that as the mass increases, the energy decreases proportionally, so a 4:1 ratio in energy corresponds to a 1:4 ratio in mass. Thus, the lighter body is more energetic under equal momentum conditions.

This option reverses the true relationship.So this option is incorrect.

This option is incorrect according to calculations.