# A particle of mass $200\;g$ is dropped from a height of $50\;m$ and another particle of mass $100\; g$ is simultaneously projected up from the ground along the same line with a speed of $100\; m/s$. The acceleration of the centre of mass after $1\; s$ is

$\begin {array} {1 1} (a)\;10\;m/s & \quad (b)\;\frac{10}{3}\;m/s^2 \\ (c)\;0 & \quad (d)\;none\;of\;these \end {array}$

$\bar {a}_{cm}=\large\frac{m_1\bar{a}_1+m_2 \bar {a}_2}{m_1+m_2}$
$\qquad=\large\frac{(m_1+m_2)g}{(m_1+m_2)}$
$\qquad=g$