Two masses ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' moving with velocities '…
Two masses ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' moving with velocities ' $\mathrm{v}_{\mathrm{a}}$ ' and ' $\mathrm{v}_{\mathrm{b}}$ ' opposite directions collide elastically. Alter the collision ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' move with velocities and ' $\mathrm{v}_{\mathrm{b}}$ ' and ' $\mathrm{v}_{\mathrm{a}}$ ' respectively, then the ratio $\mathrm{m}_{\mathrm{a}}: \mathrm{m}_{\mathrm{b}}$ is
$\frac{v_a+v_b}{v_a-v_b}$
$\frac{1}{2}$
1
$\frac{v_a-v_b}{v_a+v_b}$
Solution
When two bodies of equal masses collide elastically, they exchange their velocities. Since the two masses are exchanging their velocities, their masses must be equal.
Hence, $\frac{\mathrm{m}_{\mathrm{a}}}{\mathrm{m}_{\mathrm{b}}}=1$