A particle of mass `m_(1) = 4 kg` moving at `6hatims^(-1)`perfectly elastically with a particle of mass `m_(2) = 2` moving at `3hati ms^(-1)`

Options

A. Velocity of centre of mass (CM) is `5hatims^(-1)`
B. The velocities of the particles relative to the centre of mass have same magnitude.
C. Speed of individual particle before and after collision remains same.
D. The velocity of particles relative to CM after collisioin are `vecv_(1f//cm)=-hatims^-1,vecv_(2f//cm)=2hatims^(-1)`

Answer

A, D

Explanation

`v_(cm)=(4xx6+2xx3)/(4+2)=5ms^(-1)`
`u_(1/cm)=u_(1)-v_(cm)=6-5=1ms^(-1)`
`v_(2/cm)=u_(1)-v_(cm)=6-5=1ms^(-1)`
`v_(2/cm)=u_(1)-v_(cm)=4-5=-1ms^(-1)`
Here b in incorrect.
After collision : `v_(1)=4ms^(-1), v_(2)=7ms^(-1)`
`v_(2/cm)=v_(2)-v_(cm)=7-5=2ms^(-1)`