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.

Answer

`(##ALN_NC_PHY_NLMF_E02_008_A01##)`
(ii) `a=3//5m//s^(2),T=18N,F=60N`