question_answer

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

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

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

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

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

Correct Answer: D

Solution :

The momentum of third part will be equal and opposite to the resultant of momentum of rest of the two equal parts. Let v is the velocity of third part. By the conservation of linear momentum, \[3m\times V=m\times 12\sqrt{2}\Rightarrow v=4\sqrt{2}\,m/s\] Hence, the correction option is [d].