Actual weight of the body, W = 5kg
Apparent weight in kerosene, W' =4kg
Let the volume of the body be V and the density be ρ.
Density of kerosene = 820 kg/m 3
Buoyancy = Actual weight – Apparent weight = 5kg – 4kg = 1kg
Buoyancy = volume of kerosene displaced × density of kerosene × g
=> g = V ' ×820×g
=> V ' = 1.219× 10 -3 m 3
This is the volume of kerosene displaced.
Since, the body immerses completely, it is also the volume of the body.
So, V = V ' = 1.219× 10 -3 m 3
Now, W = 5kg
=> Vρg = 5
=> ρ = 5/(1.219 × 10 -3 m 3 ) = 4100 kg/m 3
This is the density of the body.