Q169
General SciencePhysics
A heavy body and a light body have equal kinetic energy. Then
- a.heavy body has greater momentum.
- b.light body has greater momentum.
- c.both have equal momentum.
- d.both have same angular momentum.
Answer: (A) heavy body has greater momentum.
Kinetic energy and momentum are related by $K=\frac{p^2}{2m}$, so $p=\sqrt{2mK}$. For equal $K$, $p\propto\sqrt{m}$: the heavier body has the greater momentum (though the lighter one has the greater speed). Conversely, if two bodies have equal momentum, the lighter one has the greater kinetic energy, since $K\propto\frac{1}{m}$. Example: masses of 1 kg and 4 kg with equal kinetic energy have momenta in the ratio 1 : 2. Angular momentum is not relevant here.