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In the figure , masses m(1) , m(2) and M...

In the figure , masses `m_(1) , m_(2)` and M are 20 kg , 5 kg and 50 kg respectively . The coefficient of friction between M and ground is zero . The coefficient of friction between `m_(1)` and M and that between `m_(2)` and ground is`0.4` . 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 vertical between `P_(1)` and `P_(2)` . An external horizonal force F is applied to the mass M . (Take g = `10 m //s^(2))`
(a) Draw a free body diagram for mass M , clearly showing all the forces .
(b) 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 equation of motion of all the masses . Find F , tension in the string and acceleration of the masses .

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