Three bodies P, Q and R have masses ' $\mathrm{m}$ ' $\mathrm{kg}$, ' $2 \mathrm{~m}$ ' $\mathrm{kg}$ and '…
Three bodies P, Q and R have masses ' $\mathrm{m}$ ' $\mathrm{kg}$, ' $2 \mathrm{~m}$ ' $\mathrm{kg}$ and ' $3 \mathrm{~m}$ ' $\mathrm{kg}$ respectively. If all the bodies have equal kinetic energy, then greater momentum will be for body/bodies.
Q
R
P and Q
P
Solution
Kinetic energy $\mathrm{k}=\frac{\mathrm{p}^2}{2 \mathrm{~m}}$ where $\mathrm{p}$ is the momentum
$\therefore \mathrm{p}^2=2 \mathrm{mk} \text { or } \mathrm{p}=\sqrt{2 \mathrm{mk}}$
$\therefore \mathrm{p} \propto \sqrt{\mathrm{m}}$
Hence body having greater mass will have greater momentum.