An object of mass `40kg` and having velocity `4 m//s` collides with another object of mass `60 kg` having velocity `2 m//s` . The loss of energy when the collision is perfectly inelastic is

Options

A. `392J`
B. `440J`
C. `48J`
D. `110J`

Answer

C

Explanation

Here, `m_(1)=40 kg, u_(1)=4 m//s `
`m_(2)=60 kg, u_(2)= 2 m//s`
Final vel. After collision, `upsilon=(m_(1)u_(1)+m_(2)u_(2))/((m_(1)+m_(2))) `
`upsilon=(40xx4+60xx2)/((40+60))=2.8 m//s`
Loss of energy
`=(1)/(2)m_(1)u_(1)^(2)+(1)/(2)m_(2)u_(2)^(2)-(1)/(2)(m_(1)+m_(2))upsilon^(2)`
`=(1)/(2)xx40xx4^(2)+(1)/(2)xx60xx2^(2)-(1)/(2)(40+60)xx(2.8)^(2)`
`=320+120-392=48` joule