Question

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

• A. $\sqrt{3}$
• B. $\frac{5}{\sqrt{3}}$
• C. $\sqrt{\frac{3}{2}}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{2}{\sqrt{3}}$

$F_A=\frac{\mu mg}{\cos {30}^o-\mu \sin {30}^o};F_B=\frac{\mu mg}{\cos {60}^o+\mu \sin {60}^o}$

$\frac{F_A}{F_B}$=$\frac{2}{\sqrt{3}}$