Question

Prove that the centre of mass of two particles lies on

the line joining these two particles and the ratio of

distances of particles from the centre of mass is

equal to the inverse ratio of their masses.​

Answer 1

Answer:

Hint To answer this question we should be knowing the concept of centre of mass. The centre of mass is defined as the distribution of mass in the space in a unique point where the weighted relative position of the distributed mass sums to the value of zero.

Complete step by step answer

We know that the centre of mass of the two particles that is lying on the line joining the particles.

Let us consider that the centre of mass lies at the point C.

So, we can write the expression as follows

(m1+m2)x=m1(0)+m2(L)(m1+m2)x=m1(0)+m2(L)

So, the expression of x can be written as:

x=m2Lm1+m2x=m2Lm1+m2

So, we can say that the centre of mass of two particles lies on the line joining the particles.

Hence the correct answer is option