A body of mass 1 kg moving with velocity 4 m / s collides elastically with another body of mass 2 kg moving with velocity 1 m / s in opposite direction . What are the velocities of two bodies after collision ?

1 ) A body of mass 1 kg moving with velocity 4  m / s  collides elastically with another body of mass 2 kg moving with velocity 1  m / s  in opposite direction .  What are the velocities of two bodies after collision ?

A )  v1' = - 8 / 3  m / s  and  v2' = 7 / 3  m / s ,

B )  v1' =  4 / 3  m / s  and  v2' = - 4 / 6  m / s ,

C )  v1' =  3  m / s  and  v2' = 7 m / s ,

D ) None of these ,

Correct Answer : -   A )  v1' = - 8 / 3  m / s  and  v2' = 7 / 3  m / s ,

Solution : -

2 ) Two bodies of mass 5 kg and 3 kg are moving towards each other with  2 m / s  and  4 m / s  respectively .  The velocity of centre of mass is : -

A )  0.25  m / s  towards  5 kg ,

B )  0.25  m / s  towards  3 kg ,

C )  0.25  m / s  from both sides ,   

D )  2.5  m / s  from both sides ,

Correct Answer : -   A )  0.25  m / s  towards  5 kg ,

Solution : -

So , for  5 kg : -

v = 2  m / s   =   2 î  .

So , for  3 kg : -  

v = 4  m / s   =   - 4 î  . ( because it is going in opposite direction ) .

Formula : -

v = ( m1 v1 + m2 v2 )  /  ( m1 + m2 ) ,

v = ( 5 x 2 î  +  3 x ( -4 î ) )  /  ( 5 + 3 )  ,

v = (10 î – 12 î )  /  8  ,

v =  - 0.25 î , Answer .

So ,  0.25  m / s  towards 5 kg .

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