Question

Derive an expression for the centre of mass of a two particle system from ab initio

Answer 1

Answer:

Expression of center of mass of a two particle system in easy way. ... Where m = m1 + m2, that is the mass of a hypothetical object. Its position at any time is given by position vector such that, This is nothing but the position vector and is called the centre of the mass of the two-particle system.

Answer 2

As the centre of mass lies between two particles therefore m1 = m2

R (t) = r1 (t) + r2 (t2) / 2

Explanation:

Let's say there are two masses m and m2.

According to Newton's third law.

F12 = - F12

If the velocity of masses are V1 and V2. Then

V1 = dr1 / dt and V2 = dr2 / dt

Now m1 v1 + m2v2 = m1  dr1 / dt + m2 dr2 / dt

d / dt [ m1r1 + m2r2]

F = d^2 / dt^2 [ m1r1 + m2r2]

As the centre of mass lies between two particles therefore

m1 = m2

R (t) = r1 (t) + r2 (t2) / 2