A body of mass 2m moving w ith velocity v m akes a head on elastic collision w ith another body of mass m w hich is initially at rest. Loss of kinetic energy of the colliding body (mass 2m) is

Options

A. 1/9 of its initial kinetic energy
B. 1/6 of its initial kinetic energy
C. 1/4 of its initial kinetic energy
D. 1/2 of its initial kinetic energy

Answer

C

Explanation

Initial K.E of ball of mass 2m =`k_(1)`
`=1/2xx2mxxv^(2)`
`=mv^(2)`
So K.E is conserved
`rarr v^(2)=v_(1)^(2)+1/2 v_(2)^(2)`
and momentum is conserved
`rarr2v=2v_(1)+v_(2)`
Now
`v_(2)=2(v-v_(1))`
put this value in Eq (i) we get
`v^(2)=v_(1)^(2)+1/2xx4(v-v_(1))^(2)`
`rarr3v_(1)^(2)-4vv_(1)+v^(2)=0`
so final k.e of ball of mass 2m
`k_(2)=1/2(2m)(v_(1)^(2))=1/2xx2xx(v^(2))/(9)=1/9(k_(1))`
hence loss of K.E of `I^(st)` ball
`=k_(1)-(1)/(g)k_(1)=8/9k_(1)`