question_answer

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

A) 4         

B)        6       

C) 8         

D)        10

Correct Answer: A

Solution :

The velocity of B just after collision with A is \[{{v}_{B}}=\frac{({{m}_{B}}-{{m}_{A}}){{u}_{B}}}{{{m}_{B}}+{{m}_{A}}}+\frac{2{{m}_{A}}{{u}_{A}}}{{{m}_{A}}+{{m}_{B}}}\] \[=\frac{0+2m\times 9}{m+2m}=6m/s\] The collision between B and C is completely inelastic. \[\therefore \,\,\,{{m}_{B}}{{v}_{B}}=({{m}_{B}}+{{m}_{C}})v\] \[\therefore \,\,\,v=\frac{6\times 2m}{2m+m}=4m/s.\]