Question

If a body in rest breaks up into two pieces of equal masses, then, the parts will

Answer 1

In simple terms, an object in motion changes its position, whereas an object at rest does not. Perspective, on the other hand, is extremely important. Consider an atom, which is always in motion but appears to be at rest when we see it in the macro world. As a result, both rest and motion are primarily determined by the individual's frame of reference.

Complete step by step solution:
The term "momentum" refers to the measurement of mass in motion. Any object that moves has momentum. The object's momentum equals mass times velocity, according to physics.
$Mass\text{ }\times \text{ }Velocity\text{ }=\text{ }Momentum$
Momentum is defined as the quantity of motion multiplied by the amount of matter moved and the speed at which it moves. When you walk, run, or do anything else, you're creating momentum. If a bicycle and a car both travel at the same speed down the street, the car will have the most momentum.
When a body at rest splits into two equal-mass pieces, the parts will move in opposite directions at the same speed.
According to the question,
Let the velocities of two parts be $v$ and $v'$ mass of each part =$m$.
Momentum before the break =$2m\times 0=0$
Momentum after the break= $mv+mv\prime$
Since there is no external force on the body, the linear momentum will be conserved.
$~mv+mv\prime =0~$
$v\text{ }=-v\prime ~$
So, the parts will move in opposite directions with equal speeds.

Note:
If there is no external force acting on an isolated system, its total momentum remains constant. As a result, the resultant force acting on the system is zero if the total linear momentum remains constant. In the absence of external torque, angular momentum is conserved as well.