A system consists of three masses m 1 ,   m 2 and m 3 connected by a string passing over a pulley P . The mass m 3 hangs freely and m 2 and m 1 are on a rough horizontal table (the coefficient of friction = μ ) . The pulley is frictionless and of negligible mass. The downward acceleration of mass m 3 is: (Assume m 1 = m 2 = m 3 = m )

Step-by-step solution

Let the tension force between m 1   and m 2 is T 1 and m 2 and m 3 is T 2 T 1 - μ m g = m a       . . . 1 T 2 - T 1 - μ m g = m a       . . . 2 m g - T 2 = m a       . . . 3 From equation 1 , 2   &   3 , 3 a m g = m g - 2 μ m g ⇒ a = m g - 2 μ m g 3 m g ⇒ a = g - 2 μ m g 3 = g 1 - 2 μ 3