Question

A body of mass $2kg$ is moving with velocity $10m{s}^{-1}$ towards east. Another body of the same mass and same velocity moving towards north collides with the former and coalesces and moves towards north-east. Its velocity is

• A. $10m{s}^{-1}$
• B. $5m{s}^{-1}$
• C. $2.5m{s}^{-1}$
• D. $5\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is D

$5\sqrt{2}m{s}^{-1}$

Step 1. Expressing the given data.

Mass of the first body, $m_1=m$

Mass of the second body, $m_2=m$

The initial velocity of both the body, $u=10m{s}^{-1}$

Step 2. Finding the velocity of the particle after collision, $v$

Initial Momentum, $\overrightarrow{P}=mu\hat{i}+mu\hat{j}$ [Where, $u$ is the initial velocity]

$\left|\overrightarrow{P}\right|=\sqrt{m^2{u}^2+m^2{u}^2}$

$P=\sqrt{2}mu$

$P=10\sqrt{2}m$

Final momentum$=\left(m+m\right)v$

Final momentum$=2mv$

Applying the momentum conservation,

$InitialMomentum=Finalmomentum$

$10\sqrt{2}m=2mv$

$v=5\sqrt{2}m{s}^{-1}$

Hence, the correct option is $\left(D\right)$.