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_(1)` hangs freely and `m_(2)` and `m_(3)` are on a rough horizontal table (the co efficient of fircition = p). The pulley is frictionless and of negligible mass. The downward acceleration of mass `m_(1)` is (Assume`m_(1) - m_(2) = m_(3) = m`)

Options

A. `(g(1-g mu))/(g)`
B. `(2 gmu)/(3)`
C. `(g(1-2mu))/(3)`
D. `(g(1-2mu))/(2)`

Answer

C

Explanation

`F= f_(1) - F_(2) - F_(3)`
`(m+m+m) a =m_(1)m_(1) g - mu m_(2) g - mu m_(3) g`
`3ma - mg - mu mg - mu mg`
`a= (g(1-2mu))/( 3)`