A moving `2 kg` ball with a speed of `2 ms^(-1)` hits obliquely a stationary identical ball inelastically as shown. If the first ball move away with angle `alpha = 30^(@)` to the original path, find the total kinetic energy lost after the collision

Options

A. `4//3 J`
B. `5//4 J`
C. `6//5 J`
D. `7//6 J`

Answer

A

Explanation

Tangential component remain same

`1 = (sqrt3v_(1))/(2) rArr v_(1) = (2)/(sqrt3)`
Momentum is conserved along normal
`2sqrt3 = (2 xx v_(1))/(2) + 2 xx v_(2) rArr sqrt3 = (1)/(sqrt3) + v_(2)`
`v_(2) = (2)/(sqrt3)`
`DeltaKE = (1)/(2) xx 2 xx 4 - ((1)/(2) xx 2 xx ((2)/(sqrt3))^(2) + (1)/(2) xx 2 xx ((2)/(sqrt3))^(2))`
`= (4)/(3)J`