Laws Of Motion

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