Question

A shell following a parabolic path explodes somewhere in its flight. The center of mass of fragments will continue to move in

Answer 1

Step1: Center of mass of a system of particles

1. In a system of particles, the center of mass is an imaginary point, where all the masses are concentrated.
2. The position of the center of mass of a system of particles is defined by the form, $R=\frac{{\displaystyle \sum _1^i}{m}_i{r}_i}{\sum _1^i{m}_i}$, Where, $m_i$ and $r_i$ is the mass and position of the ith particle of the system and R is the position of the center of mass.
3. If a body explodes into two pieces, then the center of mass of the body is located at, $R=\frac{m_1{r}_1+m_2{r}_2}{M}$, where, $r_1$ and $m_1$ are the position and mass of one piece, $m_2$ and $r_2$ is the position and mass of the other piece respectively.

Step 2: Finding the acceleration of the system

We know the net force applied to the explosion is zero. According to Newton's law of motion, we know that force is the product of mass $\left(m\right)$ and acceleration $\left(a\right)$, i.e, $F=ma$. When force, $F=0.$

Then

$$\begin{gathered} ma=0 \\ ora=0(\sin cemass,m\ne 0) \end{gathered}$$

Step 3: Finding the path of the center of mass

1. Change in velocity is zero, as we know acceleration is the time rate of change in velocity. So, it is clear that the motion of a body remains the same when the applied force is zero.
2. As we know, when the body explodes into multiple parts, then the net force on the system or the center of mass is zero. So, the center of mass of the system follows the same path.

Step 4: Diagram

Therefore, the center of mass of fragments will continue to move in the same parabolic path.