A solid object weighing 5kg in air, weighs 4kg in kerosene. Find (a) its volume and (b) its density

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

Now,

Buoyancy = Actual weight – Apparent weight = 5kg – 4kg = 1kg

Also,

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.

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