question_answer

Six marbles are lined Up in a straight groove made on a horizontal frictionless surface as shown below. Two similar marbles in contact, with a common velocity v collide with a row of 6 marbles from left. Which of the following is observed?

A)                 One marble from the right rolls out with a speed 2v, the remaining marbles do not move

B)                 Two marbles from the right roll out with speed v each, the remaining marbles do not move

C) All six marbles in the row will roll out with a speed v/6 each, the two incident marbles will come to rest

D) All eight marbles with start moving to die right, each with a speed of v/8

Correct Answer: B

Solution :

  This is elastic collision with 1st two marbles (A,B). Then remaining marbles (E, F, G, H) remain in rest position, and 1st two marbles at the left move with velocity v.                         \[2\,mv=2m{{v}_{1}}+2{{m}_{1}}{{v}_{2}}\] \[2v=2{{v}_{1}}+2{{v}_{2}}\] \[v={{v}_{1}}+{{v}_{2}}\]                                              ?(i)                 Also,      \[{{v}_{1}}-{{v}_{2}}=-1(v)\]                                        ?(ii) By Eqs. (i) and (ii) \[2{{v}_{1}}=0\]                 \[\therefore \]                  \[{{v}_{1}}=0\] and                        \[{{v}_{2}}=v\] Hence, option  is correct.