question_answer

A mass 3m, initially at rest at the origin, explodes into three fragments of equal mass. Two of the fragments have speed v each and move perpendicular to each other. The third fragment will move with a speed:

A)  \[v/\sqrt{2}\]                   

B)         \[v/2\]

C)  \[v\]                    

D)         \[\sqrt{2v}\]

E)  \[2v\]

Correct Answer: D

Solution :

From law of conservation of momentum \[mv-mv\cos \theta =0\]                              ?. (1) \[mv-mv\sin \theta =0\]                               ?.(2) From Eqs. (1) and (2), we get                 \[\theta =45{}^\circ \] \[\therefore \]  \[v=\frac{v}{\cos \theta }=v\sqrt{2}\]