Q. An object of mass $3m$ splits into three equal fragments. Two fragments have velocities $v\widehat{j}$ and $v\widehat{i}$. The velocity of the third fragment is
A) $v(\widehat{j} - \widehat{i})$
B) $v(\widehat{i} - \widehat{j})$
C) $- v(\widehat{i} + \widehat{j})$
D) $\frac{v(\widehat{i} + \widehat{j})}{\sqrt{2}}$
Explanation
(c) Initial momentum of $3m$ mass = 0 …(i)
Due to explosion this mass splits into three fragments of equal masses
Final momentum of system $= m\overrightarrow{V} + mv\widehat{i} + mv\widehat{j}$ …(ii)
By the law of conservation of linear momentum
$m\overrightarrow{V} + mv\widehat{i} + mv\widehat{j} = 0 \Rightarrow \overrightarrow{V} = - v(\widehat{i} + \widehat{j})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.