A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.220 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.230 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground.

Question

A lunch tray is being held in one hand, as the drawing illustrates. The mass of the tray itself is 0.220 kg, and its center of gravity is located at its geometrical center. On the tray is a 1.00 kg plate of food and a 0.230 kg cup of coffee. Obtain the force T exerted by the thumb and the force F exerted by the four fingers. Both forces act perpendicular to the tray, which is being held parallel to the ground. 
T =  N (downward)
F =  N (upward) 
the lengths are .400m, .380m, .240m, .100m, .0500m

bobpursley · Answer

There is no way this can be worked without a figure. You will have to sum moments about any point, and remember that the sum of the vertical forces will be zero. That will get you the result.