A system consists of three masses ${\mathrm{m}}_1, {\mathrm{m}}_2 \mathrm{and} {\mathrm{m}}_3$ connected by a string passing over a pulley P. The mass m, hangs freely and ${\mathrm{m}}_2$ and ${\mathrm{m}}_3$are on a rough horizontal table (the coefficient of friction = $\mathrm{\mu }$)

The pulley is frictionless and of negligible mass. The downward acceleration of mass ${\mathrm{m}}_1$ is
(Assume ${\mathrm{m}}_1 = {\mathrm{m}}_2 = {\mathrm{m}}_3$= m)

• A

  $\frac{\mathrm{g}(1-\mathrm{g\mu })}{9}$

• B

  $\frac{2\mathrm{g\mu }}{3}$

• C

  $\frac{\mathrm{g}(1-2\mathrm{\mu })}{3}$

• D

  $\frac{\mathrm{g}(1-2\mathrm{\mu })}{2}$