A spherical ball of mass `1 kg` moving with a uniform speed of `1 m//s` collides symmetrically with two identical spherical balls of mass `1 kg` each at rest touching each other. If the two balls move with `0.5 m//s` in two directions at the same angle of `60^(@)` with the direction of the first ball, the loss of kinetic energy on account of the collision is :-

Options

A. `0.125 J`
B. `0.5 J`
C. `1.0 J`
D. `0.75 J`

Answer

A

Explanation

`m xx 1 = mv_(1) + (2mv_(2) xx cos60^(@))`
`rArr v_(2) = (1)/(2)` & `v_(1) = (1)/(2)`
`(KE)_("Initial") = (1)/(2) xx 1 xx 1^(2) = 0.5 J`
`(KE)_("initial") = (1)/(2)(1) xx ((1)/(2))^(2) + {(1)/(2) xx 1 + xx ((1)/(2))^(2)}xx 2`
`= 0.25 + 0.125 = 0.3755`
`DeltaKE = 0.5 - 0.375 = 0.125 J`