# CBSE Class 11-Physics: How to Solve the Center of Mass Problems

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## What is Center of Mass & How to Solve the Center of Mass Problems

1) Center of Mass is an important concept in a system of many particles. Centre of mass is the point where whole mass of the system can be supposed to be concentrated and motion of the system can be defined in terms of the center of mass. It is the mass weighted average of its components

2) It can be calculated as

3) The co-ordinates of Center of mass depends on reference frame. But its physical location is independent of choice of the frame

## How to Solve Center of Mass Problems

Velocity and acceleration of the center of mass is given by

In the absence of external force velocity of center of mass of the system remains constant or we can say that center of mass moves with the constant velocity in absence of external force. i.e. no acceleration

The motion of the system of particles can be understood easily as translational motion of the center of mass and rotation of particles around center of mass

Four particles of same mass lie in x-y plane. The coordinates of their positions are and respectively. Find the position of the center of mass of the system

**Solution**

1) It is a simple problem, where we know the coordinates of the four particle, and we need to find CM of the system. It can be simple calculated by the formula given below

**Solution continued**

Here we are talking about plane, so we can ignore z coordinates

Also Let us assume m be the mass of each particle

Now

So

A rocket following a parabolic path in air suddenly explodes into two parts

What can be told about the center of mass of the system after explosion

a) Vertically downwards

b) Horizontally

c) It will move along the same parabolic path which the intact shell was moving

d) It will move along the tangent to the parabolic path at the point of explosion

**Solution**

We know that center of mass motion depends on the net external force. Since the net external force (Gravity) remains constant before the explosion and after the explosion, the center of mass will keep on moving in the same direction.

**Answer (c)**