Three masses $M=100 \mathrm{~kg}, m_1=10 \mathrm{~kg}$ and $m_2=20$ $\mathrm{kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass $m_2$ moves upward with an acceleration of $2 \mathrm{~ms}^{-2}$. The value of $F$ is <BR> $\left(\right.$ Take $\left.g=10 \mathrm{~ms}^{-2}\right)$ <BR>