Question

A body of mass $2kg$ moving with a velocity of $3m{s}^{-1}$ collides head-on with a body of mass $1kg$ moving in the opposite direction with a velocity of $4m{s}^{-1}$. After the collision, two bodies stick together and move with a common velocity which in $m{s}^{-1}$ is equal to

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is C

$\frac{2}{3}$

Step 1. Given data

Mass of the first body $m_1=2kg$

Mass of the second body $m_2=1kg$

Initial Velocity of the first body, $u_1=3m{s}^{-1}$

Initial Velocity of the second body, $u_2=4m{s}^{-1}$

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

As the collision is a head-on collision then both the bodies will stick to each other and move with a common velocity.

Applying the conservation of momentum that is the momentum before the collision is equal to the momentum after the collision.

$m_1{u}_1-m_2{u}_2=\left(m_1+m_2\right)v$

$2\times 3-1\times 4=\left(2+1\right)v$

$v=\frac{2}{3}m{s}^{-1}$

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