5. An interesting level controller is shown. The drain plug is closed initially. As water fills up

and the level reaches the height h, the buoyancy force on the float opens the plug.

(a) Find h (a symbolic formula). Clearly show all steps. Find the numerical value for h if

L = 10 cm, d = 10 cm, D = 20 cm, W = 3 kg and p = 1000 kg/m³.

(b) As soon as the plug opens, it is observed that the plug-float assembly jumps upwards

and attains a floating position. Briefly explain why? Determine the level in the reservoir

when the plug closes again (find symbolic expression first, and then a numeric value).

Can the plug diameter (d) be larger than the float diameter (D) for the level controller

to work? Briefly explain why or why not.