Three masses $M=100 \mathrm{~kg}, \mathrm{~m}_{1}=10 \mathrm{~kg}$ and $\mathrm{m}_{2}=20 \mathrm{~kg}$ 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 $\mathrm{F}$ is applied on the system so that the mass $\mathrm{m}_{2}$ moves upward with an acceleration of $2 \mathrm{~ms}^{-2}$. The value of $\mathrm{F}$ is :

( Take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )