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

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 :

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