The scale shown in Figure measures the weight mg of an object placed on the scale, by using a counterweight of mass mc. Friction in the pivot point at A causes the pointer to eventually come to rest at an angle θ, which indicates the measured value of the weight mg. The angle B has a fixed value that depends on the shape of the scale arm.
(a) Neglect the friction in the pivot and neglect the mass of the scale arm, and obtain the scale's equation of motion,
(b) Find the equilibrium relation between the weight mg and the angle θ.
(c) Find the weight mg if mc = 5 kg, L1 = 0.2m, L2 = 0.15 m, β = 30°, and θ = 20°.

mc