question_answer

An object of mass 3m splits into three equal fragments. Two fragments have velocities \[v\hat{j}\] and \[v\hat{i}\]. The velocity of the third fragment is                                        [UPSEAT 2004]

A)                 \[v(\hat{j}-\hat{i})\]      

B)                 \[v(\hat{i}-\hat{j})\]

C)                 \[-v(\hat{i}+\hat{j})\]   

D)                 \[\frac{v(\hat{i}+\hat{j})}{\sqrt{2}}\]

Correct Answer: C

Solution :

    Initial momentum of 3m mass = 0             ?(i) Due to explosion this mass splits into three fragments of equal masses. Final momentum of system = \[m\vec{V}+mv\hat{i}+mv\hat{j}\]             ?(ii) By the law of conservation of linear momentum \[m\vec{V}+mv\hat{i}+mv\hat{j}=0\]Þ \[\vec{V}=-v(\hat{i}+\hat{j})\]