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 coefficient of friction=`mu`). 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(1-2mu))/(2)`
B. `(g(1-gmu))/(9)`
C. `(2gmu)/(3)`
D. `(g(1-2mu))/(3)`

Answer

D

Explanation

`a=("Total driving Force")/("Total mass")=(mg-2mumg)/(3m)`
`a=g((1-2mu))/(3)`