In the figure masses m_(1),m_(2) and M are kg. 5 kg and 50 kg respectively. The co-efficient of friction between M and ground is zero. The co-efficient of friction between m_(1) and M and that between m_(2) and ground is 0.3. The pulleys and the string are massless. The string is perfectly horizontal between P_(1) and m_(1) and also between P_(2) and m_(2). The string is perfectly verticle between P_(1) and P_(2). An externam horizontal force F is applied to the mass M. Take g=10m//s^(2). (i) Drew a free-body diagram for mass M, clearly showing all the forces. (ii) Let the magnitude of the force of friction between m_(1) and M be f_(1) and that between m,_(2) and ground be f_(2). For a particular F it is found that f_(1)=2f_(2). Find f_(1) and f_(2). Write down equations of motion of all the masses. Find F, tension in the string and accelerations of the masses.