An object has a weight of 18 N in the air. Its weight is found to be 11.4 N when immersed in water. Calculate its density. Can you guess the material of the object? Ans. (2727 kgm⁻³, Aluminum) 


Given:  

Weight of an object in air  = w₁ = 18 N
Weight of an immersed object in Water  = w₂ = 11.4 N
density of water =  𝞺  = 1000 kg m⁻³
Gravitational Acceleration  = g = 10 ms⁻²
Weight of the equal volume of water displaced = w =  w₁ - w₂ = 18 N - 11.4 N = 6.6 N


To Find:

The density of the object = D = ?

Solution:   

According to Archimedes' principle, the Weight of an object in air  (w₂) is less than its actual weight of an object in air (w₁) by an amount of the weight of an equal volume of water displaced (w).

Since we have 

`\frac {D}{⍴}` = `\frac {w₁}{w}`

or 

D = `\frac {w₁}{w}` ｘ  ⍴

putting values we have

D = `\frac {18 N}{6.6 N}` ｘ 1000 kg m⁻³

D = `\frac {18000}{6.6}` kg m⁻³

D = 2727 kg m⁻³
thus, the density of the object is 2727 Kgm⁻³ which is approximately equal to the density of Aluminum. So, the Object is  Aluminum

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