question_answer

A body at rest breaks up into 3 parts. If 2 parts having equal masses fly off perpendicularly each after with a velocity of 12m/s, then the velocity of the third part which has 3 times mass of each part is                            [UPSEAT 2001]

A)          \[4\sqrt{2}\,m/s\] at an angle of \[{{45}^{o}}\] from each body

B)          \[24\sqrt{2}\,m/s\] at an angle of \[{{135}^{o}}\]from each body

C)          \[6\sqrt{2}\,m/s\] at \[{{135}^{o}}\]from each body

D)          \[4\sqrt{2}\,m/s\] at \[{{135}^{o}}\] from each body

Correct Answer: D

Solution :

The momentum of third part will be equal and opposite to the resultant of momentum of rest two equal parts let V is the velocity of third part. By the conservation of linear momentum \[3m\times V=m\times 12\sqrt{2}\]Þ \[V=4\sqrt{2}\ m/s\]