Question

A body of mass 5 kg is moving with a speed of 3 m/s collides head on with a body of mass 3kg moving in the opposite direction at a speed of 2 m/s. The first body stops after the collision. Find the final velocity of the second body.
A. $3m/s$
B. $5m/s$
C. $-9m/s$
D. $30m/s$

Answer 1

Hint:The collision is head on collision, that is it is a case of one-dimensional collision. The bodies are moving in opposite directions, and there is mention of any external force acting on the system. So, we can make use of the law of conservation of momentum to find out the final velocity of the second body.We need to take care about the direction of the motion.

Complete step by step answer:
Mass of the first body \[{{m}_{1}}=5kg\]
Mass of the second body, \[{{m}_{2}}=3kg\]
Initial velocity of first body, ${{u}_{1}}=3m/s$
The second body is moving in the opposite direction. So, taking the velocity in negative in this case
Initial velocity of second body, ${{u}_{2}}=-2m/s$
Final velocity of first body, ${{v}_{1}}=0m/s$
Let the final velocity of the second body be v.
Thus, Using the law of conservation of the momentum, we get \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\]
$\Rightarrow 5\times 3+3\times (-2)=0+3v$
$\Rightarrow 3v=9$
$\therefore v=3m/s$

So, the correct option is A.

Note:In this problem we have taken in consideration the direction of motion. If left to right is taken as positive then right to left will be taken as negative. Momentum is neither created nor destroyed. Momentum depends upon the variables mass and velocity of the body involved. This is the easiest way to solve this problem. Momentum conservation is a universal law which holds until there are no external force acts on the system. Also, there is no loss of energy taking place in the system. All the units must be in standard SI convention.