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Center of Mass : Introduction 0/4

Lecture1.1

Lecture1.2

Lecture1.3

Lecture1.4


Momentum Conservation & Collision 0/4

Lecture2.1

Lecture2.2

Lecture2.3

Lecture2.4

Center of mass of two particle system
In this chapter we will learn how to calculate Center of mass of two particles taken as a system. Let’s try to understand this by taking some examples.
As shown in about diagram, we have two particles of mass M1 and M2. Mass M1 is placed at origin and mass M2 is placed at a distance of R from origin.
Centre mass of two particle system always lies on the line joining between them.
Case 1: If M1 = 0, Rcm = r
Case 2: If M2 = 0, Rcm = 0
Case 3: If M1 = M2, Rcm = r/2
Center of mass always lies towards the heavier mass.
Q1.
Three particles of mass m, 2m & m are placed at three points as shown in the diagram. Find out distance of centre of mass from B. (i.e. from origin)
Ans:
Q2. State true or false.
Statement: Centre of mass of three particle system always lies within the triangle made by them.
Ans: TRUE
Explanation:
In this case we know that Centre of mass of mass M1 and M2 will live on the line connecting them. Now if we join this Centre of mass of mass M1 and M2 with mass M3, final Centre of mass will lie on this line. This line will always remain inside the triangle connecting the three passes.
Q3. State true or false.
Statement: Centre of mass of many particle system always lies on all within the polygon formed by them.
ANS: false.
Explanation:
In above case, we have taken for masses as shown in diagram. In such cases Centre of mass may lie outside the polygon formed by these masses.
Center of mass will lie in the largest possible polygon.