Question

In a system of two identical particles, one particle is at rest and other has acceleration 'a'. What is the acceleration of the center of mass?
1. a
2. a/2
3. 2a
4. zero

Answer 1

Correct Answer - Option 2 : a/2

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

\(a_{com}= {m_1 a_1+m_2a_2 \over m_1+m_2}\)

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

CALCULATION:

Given that a₁ = 0 and a₂ = a;  both the particles are identical so mass will be the same.

Let it is 'm'.

Acceleration of the center of mass:

\(a_{com}= {m_1 a_1+m_2a_2 \over m_1+m_2}\)

\(a_{com}= {m \times 0+m a \over m+m}\)

\(a_{com}= {ma \over 2m} = {a \over 2} \)

So the correct answer is option 2.