Answer
$42Kg$
Work Step by Step
We can find the required mass as follows:
$X_{CM}=\frac{m_cX_c+m_px_p}{m_c+m_p}$
We plug in the known values to obtain:
$4.0m=\frac{m_c(4.9m)+(63Kg)(3.4m)}{m_c+63Kg}$
$(4.0m)(m_c+(63Kg))=m_c(4.9m)+(63Kg)(3.4m)$
$m_c(4.9m-4.0m)=(63Kg)(4.0m)-(63Kg)(3.4m)$
This simplifies to:
$m_c=42Kg$
