A heavy box is to be dragged along a rough horizontal floor . To do so , person A pushes it at an angle $\;30^{0}\;$ from the horizontal and requires a minimum force $\;F_{A}\;$ , while person B pulls the box at an angle $\;60^{0}\;$ from the horizontal and needs minimum force $\;F_{B}\;$ . If the coefficient of friction between the box and the floor is $\;\large\frac{\sqrt{3}}{5}\;$, the ratio $\;\large\frac{F_{A}}{F_{B}}\;$ is :

Question

$(a)\;\sqrt{3}\qquad(b)\;\large\frac{5}{\sqrt{3}}\qquad(c)\;\sqrt{\large\frac{3}{2}}\qquad(d)\;\large\frac{2}{\sqrt{3}}$