Three masses M =100 kg, m_1=10 kg and m_2=20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are…

Three masses $\displaystyle \mathrm{M}=100 \mathrm{~kg}, \mathrm{~m}_1=10 \mathrm{~kg}$ and $\displaystyle \mathrm{m}_2=20 \mathrm{~kg}$ 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 F is applied on the system so that the mass $\displaystyle \mathrm{m}_2$ moves upward with an acceleration of $\displaystyle 2 \mathrm{~ms}^{-2}$. The value of F is : (Take $\displaystyle \mathrm{g}=10 \mathrm{~ms}^{-2}$ )