In the figure masses `m_1`, `m_2` and M are 20 kg, 5kg and 50kg 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 0.3. The pulleys and the strings 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 horizontal force F is applied to the mass M. Take `g=10m//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 equations of motion of all the masses. Find F, tension in the spring and acceleration of masses.

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 .

The coefficient of friction between m_(2) and inclined plane is mu (shown in the figure). If (m_(1))/(m_(2))=sin theta then

When force F applied on m_(2) and there is no friction between m_(1) and surface and the coefficient of friction between m_(1) and m_(2) is mu… What should be the minimum value of F so that there is no relative motion between m_(1) and m_(2)

When force F applied on m_(1) and there is no friction between m_(1) and surface and the coefficient of friction between m_(1)and m_(2) is mu. What should be the minimum value of F so that there is on relative motion between m_(1) and m_(2)

The coefficient of friction between 4 kg and 5 kg blocks is 0.2 and between 5 kg block and ground is 0.1 respectively. Choose the correct statement : (Take g=10m//s^(2) )

If coeffiecient of friction between the block of mass 2kg and table is 0.4 then out acceleration of the system and tension in the string. (g=10m//s^(2))

In fig. both pulleys and the string are massless and all the surfaces are frictionless. Given m_(1)=1kg, m_(2)= 2kg, m_(3)=3kg . Find the tension in the string