Centre Of Mass

Step 1: Using conservation of momentum.
In an explosion, the total momentum before and after the explosion is conserved. Since the body was initially stationary, the total momentum after the explosion must be zero. Thus, the momentum of the two parts must cancel each other out, giving the relationship: This can be written as:
Step 2: Relating kinetic energies.
The kinetic energy of the two parts is given by: We can express and in terms of their ratio. From the conservation of momentum, we have: Similarly, for :
Step 3: Finding the ratio.
The ratio of the kinetic energies is: Thus, the correct answer is (A) .

Step 1: Apply conservation of momentum.
Initial momentum of the body is

Step 2: Write momentum after explosion.
Mass of each part after explosion is . One part comes to rest, and the other moves with velocity .


Step 3: Solve for .

Step 1: Apply law of conservation of momentum.
Since the bodies stick together, the collision is perfectly inelastic, but momentum is conserved.
Step 2: Momentum along -axis.
Initial momentum along -axis: Step 3: Momentum along -axis.
Initial momentum along -axis: Step 4: Total mass after collision.
Step 5: Final velocity components.
Step 6: Final velocity vector.