Question

A $2kg$ mass moving with a velocity of $3m/s$ collides head-on with a body of mass $1kg$ moving in the opposite direction with a velocity of $4m/s$. After the collision, two bodies stick together and move with a common velocity which in $m/s$ 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 $m_1=2kg$

The velocity of the first body $v_1=3m/s$

Mass of the second body $m_2=1kg$

The velocity of the second body $v_2=4m/s$

Step 2: Calculate the total mass

After the collision, the two bodies stick together and move with a common velocity, the total mass can be given as,

$m=m_1+m_2$

$=2+1=3kg$

Step 3: Calculate the combined velocity

We know that linear momentum is always conserved.

Since the two bodies were initially moving in the opposite direction,

$m_1{v}_1-m_2{v}_2=mv$

$\Rightarrow v=\frac{m_1{v}_1-m_2{v}_2}{m}$

Upon substituting the values we get,

$v=\frac{2\times 3-1\times 4}{3}$

$=\frac{6-4}{3}$

$=\frac{2}{3}m/s$

Hence, the correct answer is option (C).