As shown in the figure below, we have a square one meter on a side that is free

Question

As shown in the figure below, we have a square one meter on a side that is free to rotate about an axis perpendicular to the plane of the square, a distance a from one side and a distance b from the other side. Two forces, F_1 vector and F_2 vector, are applied to diagonally opposite corners, and act along the sides ot the square, first as shown in case (i) and then as shown in case (n) of the drawing. In each case the net torque produced by the forces is zero. If the magnitude of F_2 vector if 5 times that of F_1 vector find the distances a and b that locate the axis, It should be noted that a and b .ire not drawn to scale. A =___m b =___m

Explanation / Answer

Since net torque is zero

in first case

F1*b = F2*a.................(1)

in second case

F1(1-a) = F2*b..............(2)

Also F2= 5F1................(3)

Hence

Hence b= 5a from (1) and (3)

Using (2)

1-a = 5b = 25a

Hence a = 1/26m

b = 5/26m

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