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 (Assume `m_(1)=m_(2)=m_(3)=m`).

Options

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

Answer

C

Explanation

`a=(m_(1)g-mu(m_(2)+m_(3))g)/(m_(1)m_(2)+m_(3))=(m[g-2mug])/(3m)`
`=(g)/(3)[1-2mu]` .