A metal ball of mass `2 kg` moving with speed of `36 Km//h` has a collision with a stationary ball of mass `3 kg`. If ater collision, both the ball move together, the loss in Kinetic energy due to collision is :

Options

A. `80 J`
B. `40 J`
C. ` 60 J`
D. `160 J`

Answer

C

Explanation

After collision the metal ball sticks with a stationary ball, then the Kinetic energy is lost in other forms of heat, hence in this process of in elastic collision the Kinetc energy is not conserved (only total energy is conserved) but momentum is conseved) but momentum is conserved.
From law of conservation of momentum, we have
`m_(1)u_(1)+m_(2)u_(2)=(m_(1)+m_(2))v`
`implies c=(m_(1)u_(1)+m_(2)u_(2))/((m_(1)+m_(2)))`
Given, `m=2 kg, u_(1)= 36xx5/(18)= 10m//s`,
`m_(2)= 3kg,u_(2)=0`

`:. v=(2xx10+3xx0)/(2+3)= 4 m//s`
Loss in kinetic energy is `DeltaK'-Delta-K''`
`={1/2m_(1)u_(1)^(2)+1/2m_(2)u_(2)^(2)}-{1/2(m_(1)+m_(2))v^(2)}`
`={1/2xx2xx(10)^(2)+1/2xx3xx0}`
`-{{2+3)xx1/2xx(4)}`
`= 100-40= 60J`