A hollow brass cylinder is weighed on a pan balance (kitchen scale) which read in kg. The scale reading is 5.56 kg. The brass cylinder is now removed from the scale and is replaced by a beaker of liquid density 1.56 * 10^3 kg/m^3; the scale now reads 17.50 kg. The brass cylinder is then suspended from a thread, and it is lowered into the liquid until it is completely immersed but does not touch the bottom of the beaker. The reading of the balance increases from 17.50 kg to 28.28 kg when the cylinder is immersed in the liquid. The density of brass is 8.47 * 10^3 kg/m^3.

(I) Calculate the volume of metal in the cylinder.
A=1.56

(II) Calculate the upthrust (buoyancy force) exerted on the hollow cylinder when it is totally immersed in the liquid.

(III) Calculate the volume of the hollow space inside the cylinder.

Please help on II and III

To calculate the upthrust (buoyancy force) exerted on the hollow cylinder when it is totally immersed in the liquid, we can use Archimedes' principle.

The buoyancy force (F_b) experienced by an object immersed in a fluid is equal to the weight of the fluid displaced by the object. It can be calculated using the formula F_b = ρ_fluid * g * V_displaced, where ρ_fluid is the density of the fluid, g is the acceleration due to gravity, and V_displaced is the volume of the fluid displaced by the object.

In this case, the density of the fluid (liquid) is given as 1.56 * 10^3 kg/m^3, and the volume of the fluid displaced by the hollow brass cylinder is equal to the volume of the cylinder itself.

The mass of the brass cylinder can be calculated by subtracting the mass of the liquid from the combined mass of the liquid and the brass cylinder. We have the readings from the pan balance as follows:
Initial reading: 17.50 kg
Reading after immersing the brass cylinder: 28.28 kg

Therefore, the mass of the brass cylinder is (28.28 kg - 17.50 kg) = 10.78 kg.

We can calculate the volume of metal in the cylinder using the formula:
Volume = Mass / Density = 10.78 kg / (8.47 * 10^3 kg/m^3).

For Part II of the question, we need to calculate the buoyancy force exerted on the hollow cylinder when it is totally immersed in the liquid. The volume of fluid displaced is equal to the volume of the metal in the cylinder, which we calculated previously.

Buoyancy Force (F_b) = Density of fluid (ρ_fluid) * g * Volume of fluid displaced
F_b = (1.56 * 10^3 kg/m^3) * 9.8 m/s^2 * Volume of metal in cylinder

To calculate Part III, we need to find the volume of the hollow space inside the cylinder. This can be done by subtracting the volume of the metal in the cylinder from the total volume of the cylinder.

Total Volume of Cylinder = Volume of Metal in Cylinder + Volume of Hollow Space

Therefore, Volume of Hollow Space = Total Volume of Cylinder - Volume of Metal in Cylinder.

To calculate the upthrust (buoyancy force) exerted on the hollow cylinder when it is totally immersed in the liquid, we can use Archimedes' Principle. According to Archimedes' Principle, the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

The weight of the liquid displaced by the hollow cylinder can be calculated as follows:

Weight of the liquid = Volume of the liquid * Density of the liquid * Acceleration due to gravity

From the question, we are given the density of the liquid (1.56 * 10^3 kg/m^3) and the change in scale reading when the cylinder is immersed in the liquid (28.28 kg - 17.50 kg = 10.78 kg).

To find the volume of the liquid displaced by the cylinder, we need to first find the mass of the liquid displaced.
We know that weight = mass * acceleration due to gravity, so rearranging this equation gives us: mass = weight / acceleration due to gravity.

The mass of the liquid displaced by the cylinder can be found as follows:

Mass of the liquid = Weight of the liquid / Acceleration due to gravity

Now, we can calculate the volume of the liquid displaced by the hollow cylinder using the formula:

Volume of the liquid = Mass of the liquid / Density of the liquid

Solving these calculations using the given values, we can find the upthrust (buoyancy force) exerted on the hollow cylinder when it is totally immersed in the liquid.

To calculate the volume of the hollow space inside the cylinder (III), we can subtract the volume of the metal in the cylinder (I) from the total volume of the cylinder.

The total volume of the cylinder can be calculated using its mass (taken from the scale reading) divided by the density of the brass.

Finally, subtracting the volume of the metal from the total volume will give us the volume of the hollow space inside the cylinder.