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
(a) zero
(b)
(c)
(d)

Answer 1

(b) $\frac{1}{2}\overrightarrow{a}$

Acceleration of centre of mass of a two-particle system is given as,
${\overrightarrow{a}}_{cm}=\frac{m_1{{\displaystyle \overrightarrow{a}}}_1+m_2{\displaystyle \overrightarrow{a_2}}}{m_1+m_2}$ ...(1)

According to the question,

$$\begin{gathered} m_1=m_2=m \\ {a}_1=0 \\ {a}_2=a \end{gathered}$$

Substituting these values in equation (1), we get:
${\overrightarrow{a}}_{cm}=\frac{m\times 0+m{\displaystyle \overrightarrow{a}}}{2m}=\frac{1}{2}\overrightarrow{a}$