Question

Two bodies A and B of masses m and M (M>>m) have same kinetic energy.Which body will have more momentum?

Answer 1

Given that, the kinetic energy of the two bodies is equal.

That is,

$\frac{1}{2}m{v}^2=\frac{1}{2}M{V}^2\Rightarrow \frac{V^2}{v^2}=\frac{m}{M}\Rightarrow \frac{V}{v}=\sqrt{\frac{m}{M}}$

Linear momentum is given by,

$p=mvP=MV$

$\frac{P}{p}=\frac{MV}{mv}=\frac{M}{m}\sqrt{\frac{m}{M}}$

Therefore,

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

That is mass has a direct dependence on linear momentum.

Hence, the heavier body, M will have a greater momentum.