(Solved): 1. (Outcome 2) A liquid-level control device is shown in the figure. When the liquid level ...

1. (Outcome 2) A liquid-level control device is shown in the figure. When the liquid level rises above a desired height, $h_0$, the device lifts and allows liquid to drain out through the hole in the bottom of the tank. After a certain amount of liquid drains, the device falls, and the plug seals the hole. The plug (diameter $D_p$ ) and float (diameter $D_f$ ) are connected by a rod of length $L$. (a) (b) Liquid level control device. The flost diameter $D_f=0.18\mathrm{m}$, the rod length $L=0.4\mathrm{m}$, and the weight of the device (including flost, plug, and rod) $W=20\mathrm{N}$. The thickness of the plug is very small so that its height is effectively zero. (a) The desired liquid level $h_0=0.5\mathrm{m}$. What would the plug diameter have to be so that the device just lifte when the level reaches ho? The liquid is water with $p=1000\mathrm{kg}/{\mathrm{m}}^3$. (b) Once the liquid level reaches $h_0=0.5\mathrm{m}$, the device rises and floats. For the values given above, what would be the depth $d$ of the float when the water level is at ho? Note: you do not hava to complete part (a) in order to do part (b).