A block of mass $m=2 \mathrm{kg}$ is placed on a plank of mass $M=10 \mathrm{kg},$ which is placed on a smooth horizontal plane, as shown in the figure. The coefficient of friction between the block and the plank is $\mu =\frac{1}{3}$ . If a horizontal force $F$ is applied on the plank, then the maximum value of $F$ for which the block and the plank move together is $\left(g=10 \mathrm{m}/{\mathrm{s}}^2\right)$