A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the 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. `56%`
B. `62%`
C. `44%`
D. `50%`

Answer

A

Explanation

Kinetic energy `= (1)/(2)m(2v)^(2) xx (1)/(2)2m(v)^(2)`
After collison
Applying momentum conservation for inelastic collision
`2mv hat(j) + m2vhat(i) = 3mvec(v)_(i)`
`K_(f) = (1)/(2) xx 3m xx (v_(f)^(2)) = (4mv^(2))/(3)`
`% DeltaK = (K_(1) - K_(f))/(K_(i))`