question_answer

A body is moving with a velocity v, breaks up into two equal parts. One of the part retraces back with velocity v. Then the velocity of the other part is                                 [DCE 2004]

A)                 v in forward direction    

B)                 3v in forward direction

C)                 v in backward direction

D)                 3v in backward direction

Correct Answer: B

Solution :

                    Let the initial mass of body = m Initial linear momentum = \[mv\]             ?(i) When it breaks into equal masses then one of the fragment retrace back with same velocity                 \ Final linear momentum = \[\frac{m}{2}(-v)+\frac{m}{2}({{v}_{2}})\]    ?(ii)                 By the conservation of linear momentum                 Þ \[mv=\frac{-mv}{2}+\frac{m{{v}_{2}}}{2}\]Þ \[{{v}_{2}}=3v\]                 i.e. other fragment moves with velocity 3v in forward direction