A light rod connects two masses M₁ and M₂ , and the system is slipping down a rough incline making an angle with the horizontal. If the friction coefficient at both contacts is , determine the acceleration of the system and the force exerted by the rod on one of the blocks.

Step-by-step solution

Let a be the common acceleration of the system and T be the force exerted by the rod. The equations of motion for the two masses along the incline are: M₁ g - M₁ g + T = M₁ a M₂ g - M₂ g - T = M₂ a Adding the two equations, we get: (M₁ + M₂) g - (M₁ + M₂) g = (M₁ + M₂) a a = g( - ) Substituting the value of a in the first equation: M₁ g - M₁ g + T = M₁ g( - ) T = 0 Thus, the acceleration of the system is g( - ) and the force exerted by the rod is zero.