A heavy box is to be dragged along a rough horizontal floor. To do so, the person A pushes it at an angle 30 ° from the horizontal and requires a minimum force F A , while the 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 3 5 , the ratio F A F B is

Step-by-step solution

F A cos 30 ° = μ m g + F A sin 30 ° F B cos 60 ° = μ m g - F B sin 60 ° F A cos 30 ° - μ sin 30 ° = μ m g F B cos 60 ° + μ sin 60 ° = μ m g Divide the equation, we get, ⇒ F A F B = μ m g / cos 30 ° - μ sin 30 ° μ m g / cos 60 ° + μ sin 60 ° = 2 3