Question

In a system of two identical particles, both are moving towards each other with speed 'v'. What is the speed of the center of mass?
1. 2v
2. v
3. 4v
4. center of mass will not move anywhere.

Answer 1

Correct Answer - Option 4 : center of mass will not move anywhere.

CONCEPT:

• Center of mass: Centre of the mass of a body is a point at which the whole of the mass of the body appeared to be concentrated.

The velocity of the center of mass of a two-body system is calculated by: 

\(v_{com}= {m_1 v_1+m_2 v_2 \over m_1+m_2}\)

where acom is the acceleration of the center of mass, m1 and m2 are the masses of two bodies, a1 and a2 are accelerations.

CALCULATION:

Given that v1 = v and v2 = -v (opposite direction);  both the particles are identical so mass will be the same.

Let it is 'm'.

The velocity of the center of mass:

\(v_{com}= {m_1 v_1+m_2 v_2 \over m_1+m_2}\)

\(v_{com}= {m \times v+m (-v) \over m+m}\)

v_com = 0

So the correct answer is option 4.