Question

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

• A. $\frac{2}{3}m{s}^{-1}$
• B. $\frac{3}{4}m{s}^{-1}$
• C. $\frac{1}{4}m{s}^{-1}$
• D. $\frac{1}{3}m{s}^{-1}$

Answer 1

The correct option is A $\frac{2}{3}m{s}^{-1}$

Here, a body of mass 2 kg moving with a velocity of $3m{s}^{-1}$ collides head on with a body of mass 1 kg moving with a velocity of $4m{s}^{-1}$ in opposite direction. After collision the two bodies stick together and move with a common velocity.
We can write,
$m_1{u}_1-m_2{u}_2=(m_1+m_2)v$
$\left(2\right)\left(3\right)-\left(1\right)\left(4\right)=(2+1)v$
$2=3v$
$\Rightarrow v=\frac{2}{3}m{s}^{-1}$