Two masses ma and mb moving with velocities va and vb in opposite direction collide elastically and after the collision ma and mb move with velocities vb and va respectively. Then the ratio (ma/mb) is

Question

Two masses ma and mb moving with velocities va and vb in opposite direction collide elastically and after the collision ma and mb move with velocities vb and va respectively. Then the ratio (ma/mb) is (A) (va-vb/va+vb) (B) (va+vb/va-vb) (C) 1 (D) (1/2)

Tardigrade Admin · Accepted Answer

As velocities are exchanged on perfectly elastic collision, therefore, masses of two objects must be equal. ∴ (ma/mb)=1 or ma=mb

Q. Two masses $m_{a}$ and $m_{b}$ moving with velocities $v_{a}$ and $v_{b}$ in opposite direction collide elastically and after the collision $m_{a}$ and $m_{b}$ move with velocities $v_{b}$ and $v_{a}$ respectively. Then the ratio $\frac{m _{a}}{m _{b}}$ is

$\frac{v _{a} - v _{b}}{v _{a} + v _{b}}$

$\frac{v _{a} + v _{b}}{v _{a} - v _{b}}$

1

$\frac{1}{2}$

As velocities are exchanged on perfectly elastic collision, therefore, masses of two objects must be equal.
$∴ \frac{m _{a}}{m _{b}} = 1$ or $m_{a} = m_{b}$

Q. Two masses ma​ and mb​ moving with velocities va​ and vb​ in opposite direction collide elastically and after the collision ma​ and mb​ move with velocities vb​ and va​ respectively. Then the ratio mb​ma​​ is

va​+vb​va​−vb​​

va​−vb​va​+vb​​

1

21​

As velocities are exchanged on perfectly elastic collision, therefore, masses of two objects must be equal. ∴mb​ma​​=1 or ma​=mb​

Q. Two masses $m_{a}$ and $m_{b}$ moving with velocities $v_{a}$ and $v_{b}$ in opposite direction collide elastically and after the collision $m_{a}$ and $m_{b}$ move with velocities $v_{b}$ and $v_{a}$ respectively. Then the ratio $\frac{m _{a}}{m _{b}}$ is

$\frac{v _{a} - v _{b}}{v _{a} + v _{b}}$

$\frac{v _{a} + v _{b}}{v _{a} - v _{b}}$

$\frac{1}{2}$

As velocities are exchanged on perfectly elastic collision, therefore, masses of two objects must be equal.
$∴ \frac{m _{a}}{m _{b}} = 1$ or $m_{a} = m_{b}$