Question

Two masses ${\text{m}}_1$ and ${\text{m}}_2$ collide with each other. Before the collision, the velocities are ${\text{u}}_1$ and ${\text{u}}_2$ respectively. After the collision, the velocities are ${\text{v}}_1$ and ${\text{v}}_2$ respectively. The total final momentum after collision is given by:

• A. ${\text{m}}_1{\text{v}}_2+{\text{m}}_2{\text{v}}_1$
• B. ${\text{m}}_1{\text{u}}_2+{\text{m}}_2{\text{u}}_1$
• C. ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2$
• D. ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{v}}_2$

Answer 1

The correct option is C ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2$

The initial momentum of body of mass ${\text{m}}_1$ = ${\text{m}}_1{\text{u}}_1$
The initial momentum of body of mass ${\text{m}}_2$ = ${\text{m}}_2{\text{u}}_2$
Total initial momentum before collision = ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2$
According to the law of conservation of momentum, the total momentum of a system is always conserved, i.e. the initial momentum is equal to the final momentum.
So we can say the total final momentum = ${\text{m}}_1{\text{v}}_1+{\text{m}}_2{\text{v}}_2=$ the total initial momentum = ${\text{m}}_1{\text{u}}_1+{\text{m}}_2{\text{u}}_2$