Your employer tasked you to design a draining system for a water tank using your CE$3603$ knowledge. The goal is to design a system that starts draining the tank when the water level in the tank increases to a certain level. You came up with the draining system design as shown in the schematic. The system consists of a Cube that serves as a drain plug, a cylindrical Buoy, and a Lever that is connected to a hinge at the side wall and the Buoy and the Cube through cables as shown. The Lever is a rectangular prism in shape with the dimensions of $5cm5cm50cm$ and has a uniform density of ${}_L=600k\frac{g}{m^3}.$ The Cube has a mass of $1kg$ and side length of $3cm.$ The Buoy has a diameter of $3cm$ and assume that it is always vertical and stable as shown in the schematic. Horizontal Lever $($i$.$e$.$ the instant shown in the schematic$)$ occurs right before the drain system opens, and when the water level increases, the Lever rotates counter$-$clockwise and water starts draining from the tank bottom. Assuming that the water density is ${}_w=1000k\frac{g}{m^3}$ :

a$)$ What is the value of submergence depth, $h,($see the schematic$)$ for negligible mass of Buoy?

b$)$ What is the value of $h$ if the Buoy has a mass of $0\mathrm{.}1kg?$