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. 0.5
B. 0.56
C. 0.62
D. 0.44

Answer

D

Explanation

Conservation of linear momentum along X - aixs
`m2v + 2m(0) = (2m+m)V_(x)`
Conservation of linear momentum along Y - aixs ,
`2mv+m(0)=(2m+m)V_(y)`
Final velocity of stuck bodies
`v. = sqrt((V_(x)^(2)+V_(y)^(2)) = sqrt((2/3v)^(2)+(2/3v)^(2))`
`K.E_("initial") =1/2 m(2v)^(2)+1/22m(v)^(2)=3mv^(2)`
`K.E_("final") = 1/2 3mv^(2) =1/2 3m(4/9v^(2)+4/9v^(2))`
`=4/3mv^(2)`
` :. ` Fractional loss = `(3-4/3)/3 = 5/9 = 0.56 % `
% of fractional loss ` = 5/9 xx100 = 56 % `