Motion of Center of Mass: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Motion of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:

The acceleration of the centre of mass is given by \( a_{\text{cm}} = \frac{m_1 a_1 + m_2 a_2}{m_1 + m_2} \). Since \( m_1 = m_2 = m \), \( a_1 = 0 \), and \( a_2 = a \), we get \( a_{\text{cm}} = \frac{m(0) + m(a)}{2m} = \frac{a}{2} \).