Q. A particle of mass $m$ moving eastward with a speed $v$ collides with another particle of the same mass moving northward with the same speed $v$. The two particles coalesce on collision. The new particle of mass $2m$ will move in the north-easterly direction with a velocity
A) $v/2$
B) $2v$
C) $v/\sqrt{2}$
D) $v$
Explanation
(c) Initial momentum of the system
${\overrightarrow{p}}_{1} = mv\widehat{i} + mv\widehat{j} \Rightarrow \left| {\overrightarrow{P}}_{i} \right| = \sqrt{2}mv$
Final momentum of the system $= 2mV$
By the law of conservation of momentum
$\sqrt{2}mv = 2mV \Rightarrow V = \frac{v}{\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.