Question

Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an Acceleration

Options

• zero

• \[\frac{1}{2} \vec{a}\]

• \[\vec{a}\]

• \[2 \vec{a}\]

Answer 1

\[\frac{1}{2} \vec{a}\]
Acceleration of centre of mass of a two-particle system is given as,
\[\vec{a}_{cm} = \frac{m_1 \vec{a}_1 + m_2 \vec{a_2}}{m_1 + m_2}\]     ..............(1)
According to the question,
\[m_1 = m_2 = m\]
\[ a_1 = 0\]
\[ a_2 = a\]
Substituting these values in equation (1), we get:
\[\vec{a}_{cm} = \frac{m \times 0 + m \vec{a}}{2m} = \frac{1}{2} \vec{a}\]