Q. An object at rest in space suddenly explodes into three parts of same mass. The momentum of the two parts are $2p\widehat{\mathbf{i}}$ and $p\widehat{\mathbf{j}}$. The momentum of the third part
A) Will have a magnitude $p\sqrt{3}$
B) Will have a magnitude $p\sqrt{5}$
C) Will have a magnitude $p$
D) Will have a magnitude $2p$
Explanation
(b) Combined momentum $= 2p\widehat{\mathbf{i}} + p\widehat{\mathbf{j}}$
Magnitude of combined momentum
$= \sqrt{(2p)^{2} + p^{2}} = \sqrt{5p^{2}} = \sqrt{5}p$
This must be equal to the momentum of the third part
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.