Two masses of 1 gram and 4 gram are moving with equal kinetic energy. The ratio of the magnitudes of their…
Two masses of 1 gram and 4 gram are moving with equal kinetic energy. The ratio
of the magnitudes of their momenta is
$4: 1$
$\sqrt{2}: 1$
$1: 2$
$1: 16$
Solution
Kinetic energy $\mathrm{K}=\frac{\mathrm{p}^{2}}{2 \mathrm{~m}}$
Two masses are given as- $\mathrm{m}_{1}=1 \mathrm{gm}$ and $\mathrm{m}_{2}=4 \mathrm{gm}$
But $\mathrm{K}_{1}=\mathrm{K}_{2}$
$\therefore \frac{\mathrm{p}_{1}^{2}}{2 \mathrm{~m}_{1}}=\frac{\mathrm{P}_{2}^{2}}{2 \mathrm{~m}_{2}}$
Or $\frac{\mathrm{P}_{1}^{2}}{2(1)}=\frac{\mathrm{P}_{2}^{2}}{2(4)}$
$\Longrightarrow \mathrm{P}_{1}: \mathrm{P}_{2}=1: 2$