question_answer

A body of mass a, moving with a velocity b collides with a body of mass c, at rest and sticks to it. They move together with a velocity given by:

A) \[\frac{ac}{a+b}\]                                           

B)        \[\frac{ab}{a+c}\]

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

D)        \[\frac{b+c}{ab}\]

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 \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=({{m}_{1}}+{{m}_{2}})v\]                            Given, \[{{m}_{1}}=a,{{v}_{1}}=b,{{m}_{2}}=c,{{v}_{2}}=0\]                 \[\therefore \]  \[a.b+c.0=(a+c)v\]                 \[\Rightarrow \]               \[v=\frac{ab}{a+c}\]