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) \[\frac{v}{\sqrt{2}}\]                                     

B) \[\frac{v}{2}\]

C) \[v\]                     

D)        \[v\sqrt{2}\]

Correct Answer: D

Solution :

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