Question

A particle of mass `m`, kinetic energy `K` and momentum `p` collides head on elastically with another particle of mass `2 m` at rest. After collision, :
`{:(,"Column I",,"Column II",),((A),"Momentum of first particle",(p),3//4 p,),((B),"Momentum of second particle",(q),-K//9,),((C ),"Kinetic energy of first particle",(r ),-p//3,),((D),"Kinetic energy of second particle",(s),(8K)/(9),),(,,(t),"None",):}`

Answer 1

Correct Answer - A `rightarrow` r, B `rightarrow`t, D `rightarrow` s
`p_(1)+p_(2) = p`

Further, `K_(1) + K_(2) = K`
or `p_(1)^(2)/(2m)+p_(2)^(2)/(4m) = p^(2)/(2m)`
or `2p_(1)^(2) + p_(2)^(2) = 2p^(2)`
Solving Eqs. (i) and (ii), we get
`p_(2) = 4/3 p` and `p_(1) = -p/2, K_(1) = K/9`
and `K_(2) = (8K)/9`