Question

Let be a cylindrical box with a volume of 1200cm^3 and a weight of 0.13kg. 

-What is the maximum mass of lead that we can put in the box without it being submerged in water? 
 
The density of lead is 11.4 t/m3.

Can you comment how is it incomplete, What is missing?

Answer 1

An object is submerged in water if its density is greater than the density of water. It will float if its density is lesser than the density of water.

The volume of the cylindrical box is

Using 1cm=10^-2m we get

The mass of the empty box is

The density of the cylindrical box as a whole when it is empty is

The density of the empty box is less than the density of the water (1000 kg/m³). Therefore, the empty box will float in water.

We want to determine the maximum mass of the lead that we can put into the box and the box still floats. Let m_lead be the mass of the lead that we put into the box. The total mass of the box as a whole is

The density of the box is

The box floats if the density is less than the density of water

Substituting values

The maximum mass of the lead that we can put into the box and the box still floats is

Now, we will check whether this amount of lead can be put into the box. We will calculate the volume of 1.07kg of lead and check if its less than the volume of the box which is 1200cm³.

Given density of the lead is

The mass of the lead in grams is m_lead,max=1070g

The volume of the lead is

The volume of the lead is less than the capacity of the box. Therefore, 1.07kg is the maximum mass that can be put into the box and the box still floats.