A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in they y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to :

Options

A. `44%`
B. `50%`
C. `56%`
D. `62%`

Answer

C

Explanation

For perfectly inelastic collision
`:.` Initial momentum
`sqrt((m( upsilon))^(2)++{2m(upsilon)^(2)}=2sqrt(2))m upsilon`
final momentum `=(2m+m) V=2mV`
As momentum is conserved
final momentum `=` Initial momentum
`3mV=2sqrt(2)m upsilon`
`V=(2sqrt(2)upsilon)/(3)`
Initial `KE=(1)/(2)m(2upsilon)^(2)+(1)/(2)(2m)upsilon^(2)=3 m upsilon^(2)`
Final `KE=(1)/(2)(3m)V^(2)=(1)/(2)(3m)((2sqrt(2))/(3)upsilon)^(2)`
`=(4)/(3)m upsilon^(2)`
Loss of energy `(m upsilon^(2)-(4)/(3)m upsilon^(2))/(3 m upsilon^(2))xx100`
`=(500)/(9)=55.5%=56%`