Question

When a light and a heavy body have equal K.E., then which one has a greater momentum?

• A. Light body
• B. Heavy body
• C. Both have equal momentum
• D. Uncertain

Answer 1

Answer: (B)

Heavy body

Let us analyse these two cases by assuming the mass of the lighter body to be m and heavier body to be M. If p and P are the momentums of the lighter and heavier bodies respectively, then their kinetic energies may be expressed as:

$\frac{p^2}{2m}=\frac{P^2}{2M}$

or, $\frac{p}{P}=\sqrt{\frac{m}{M}}$

or, $p=P\sqrt{\frac{m}{M}}$ and $P=p\sqrt{\frac{M}{m}}$

Thus from these equations we can conclude that the heavier mass, $M$ has greater momentum $P$.