A heavy box is to be dragged along a rough horizontal floor. To do so, person $A$ pushes it at an angle $30°$ from the horizontal and requires a minimum force $F_A$, while person $B$ pulls the box at an angle $60°$ from the horizontal and needs minimum force $F_B$. If the coefficient of friction between the box and the floor is $\frac{\sqrt{3}}{5}\text{,}$ the ratio $\frac{F_A}{F_B}$ is :

A $30 \mathrm{kg}$ slab B rests on a frictionless floor as shown in the figure. A $10 \mathrm{kg}$ block A rests on top of the slab- B. The coefficients of static and kinetic friction between the block A and the slab B are $0.60$ and $0.40$ respectively. When block-A is acted upon by a horizontal force of $100 \mathrm{N}$, as shown, find the resulting acceleration of the slab- B. $\left(\mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

As shown in the figure, a block of mass $\sqrt{3} \mathrm{kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60°$ with horizontal such that it does not move, will be $3x$. The value of $x$ will 

$\left[g=10 \mathrm{m} {\mathrm{s}}^{-2}; \sin 60°=\frac{\sqrt{3}}{2}; \cos 60°=\frac{1}{2}\right]$

The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _______$\mathrm{N}$ (take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$