A beaker of mass m-beaker containing oil of mass m-oil (density = p-oil) rests on a scale. A block of iron of mass m-iron is suspended from a spring scale and completely submerged in the oil. Determine the equilibrium readings of both scales.
''I know the iron mass will experience the force of gravity and a buoyant force.''
That's correct, but don't forget that the spring scale also exerts a force on the iron mass. The reading of the spring scale is in fact precisely this force (up to conversion factors if e.g. the scale is calibrated to show mass instead of weight). The amount by which the spring has stretched determines the force exerted on the string and from action = - reaction this is also the force exerted by the spring.
In equilibrium the total force exerted on the iron mass must be zero. So we can write: ...
A detailed solution is given.