question_answer

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

A) 110J                                      

B) 48J

C) 392J                                      

D) 440J

Correct Answer: B

Solution :

Key Idea: In inelastic collision linear momentum is conserved. If two bodies stick together after the collision, the collision is said to be perfectly inelastic. In this collision most of the kinetic energy is lost  in other forms specially heat. Thus, in an inelastic collision the kinetic energy is not conserved but total energy and momentum is conserved. Form law of conservation of momentum, we have \[{{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}=({{m}_{1}}+{{m}_{2}})v\] \[\Rightarrow \]   \[40\times 4+60\times 2=(40+60)v\] \[\Rightarrow \]\[160+120=100v\] \[\Rightarrow \]\[v=\frac{280}{100}=2.8\,m/s\] Also kinetic energy is lost, this appears as heat. This decrease is given by \[=\frac{1}{2}\times 40\times {{(4)}^{2}}+\frac{1}{2}\times 60\times {{(2)}^{2}}\] \[-\frac{1}{2}\times 100\times {{(2.8)}^{2}}\] \[=320+120-392\] \[=48\,J\]