Question

What are the volume and the density of an object with apparent weights of 403 N in air and 264 N when immersed in alcohol? The density of alcohol is 0.70 g/cm^3 and the density of air is 0.0012 g/cm^3.

Answer 1

`V=2.026*10^4cm^3`

`\rho=2.03(g)/(cm^3)`

Step-by-step explanation:

By the Archimedes principle we know that every body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

Due to this, the object has a loss weight when immersed in alcohol of:

`403N-264N=139N`

So, we can find the displaced mass of alcohol:

`m=(W)/(g)\\m=(139N)/(9.8(m)/(s^2))\\m=14.18kg`

Now, we calculate the displaced volume of alcohol, which is the same volume of the object:

`V=(m)/(\rho)\\V=(14.18*10^3g)/(0.7(g)/(cm^3))\\V=2.026*10^4cm^3`

Object mass is:

`m=(W)/(g)\\m=(403N)/(9.8)=41.12kg`

Finally, we can find the density of the object:

`\rho=(m)/(V)\\\rho=(41.12*10^3g)/(2.025*10^4cm^3)\\\rho=2.03(g)/(cm^3)`