question_answer

A body of mass a moving with a velocity b strikes a body of mass c and gets embebded into it- The velocity of the system after collision is :

A) \[\frac{a+c}{ab}\]                           

B) \[\frac{ab}{a+c}\]

C) \[\frac{a}{b+c}\]                              

D) \[\frac{a}{a+b}\]

Correct Answer: B

Solution :

                 Key Idea: In inelastic collision momentum remains conserved. Macroscopic collisions are generally inelastic  and do not conserve kinetic energy, though of course the total energy is conserved. The extreme inelastic collision is one in which the colliding objects stick together after collision. From conservation of momentum, we have From conservation of momentum, we have \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=({{m}_{1}}+{{m}_{2}})v\] Given, \[{{m}_{1}}=a,{{v}_{1}}=b,{{m}_{2}}=c,\,{{v}_{2}}=0\] \[\therefore \]      \[a.b+c.0=(a+c)v\] \[\Rightarrow \]             \[v=\frac{ab}{a+c}\]