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 \[\theta ={{45}^{o}}\] \[v\frac{v}{\cos \theta }=v\sqrt{2}\]