Question

A body of mass $2kg$ is moving with velocity $10m/s$ towards east. Another body of same mass and same velocity moving towards north collides with former and coalsces and moves towards north-east. Its velocity is

• A. $10m/s$
• B. $5m/s$
• C. $2.5m/s$
• D. $5\sqrt{2}m/s$

Answer 1

The correct option is D $5\sqrt{2}m/s$

There is no external force, so we can apply momentum conservation.

initial momentum $=\overrightarrow{P}=mv\hat{i}+mv\hat{j}$

$|\overrightarrow{P}|=\sqrt{2}mv$

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 $v=10m/s$ (given )

$\therefore V=\frac{10}{\sqrt{2}}=5\sqrt{2}m/s$