Particle 1 experiences a perfectly elastic collision with a stationary particle 2. Determine their mass ratio, if
(a) after a head-on collision the particles fly apart in the opposite directions with equal velocities,
(b) the particles fly apart symmetrically relative to the initial motion direction of particle I with the angle of divergence `theta=60^@`.

Answer

`(m_(2))/(m_(1))=3`

Explanation

Collision is perfectly elastic collision, particle 2 is at rest `(u_(2)=0)`
`V_(1)=-V_(2)(` given `)`
`(A)((m_(1)-m_(2))u_(1))/((m_(1)+m_(2)))=(-2m_(1)u_(1))/((m_(1)+m_(2)))`
`m_(1)-m_(2)=-2m_(1)=3m_(1)=m_(2)`
`(m_(1))/(m_(2))=(1)/(3)`