A system consists of three masses `m_(1)` , `m_(1)` , `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 coefficient of friction=mu) The pulley is frictionless and of negligible mass. The downward acceleration of m`1` is (Assume `m_(1)=m_(2)=m_(3)=m`).

Options

A. `(2 g mu)/(3)`
B. `(g(1 - 2 mu))/(3)`
C. `(g(1- 2mu))/(2)`
D. `(g(1 - g mu))/(9)`

Answer

B

Explanation

`mg - mu mg - mu mg = ( m + m + m)a`
`g( 1 - 2 mu) = 3a`
`a = (g( 1 - 2 mu))/(3)`