Q. A body of mass $2\ kg$ is moving with velocity $10\ m/s$ towards east. Another body of same mass and same velocity moving towards north collides with former and coalesces and moves towards north-east. Its velocity is
A) $10\ m/s$
B) $5\ m/s$
C) $2.5\ m/s$
D) $5\sqrt{2}\ m/s$
Explanation
(d) Initial momentum $= \overrightarrow{P} = mv\widehat{i} + mv\widehat{j}$
$\left| \overrightarrow{P} \right| = \sqrt{2}mv$
Final momentum $= 2m \times V$
By the law of conservation of momentum
$2m \times V = \sqrt{2}\ mv \Rightarrow V = \frac{v}{\sqrt{2}}$
In the problem $v = 10\ m/s$ [Given] $\therefore V = \frac{10}{\sqrt{2}} = 5\sqrt{2}\ m/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.